Dynamics Questions Test 2

Total Questions:50 Total Time: 60 Min

Remaining:

 

Questions 1 of 50

Question:If the law of motion of a particle moving in a straight line is given by \(ks = \log \left( {\frac{1}{v}} \right)\), then its acceleration a is given by

Answers Choices:

\(a = - kv\)

\(a = - k{v^3}\)

\(a = - k{v^2}\)

None of these

Questions 2 of 50

Question:A point moves rectilinearly with deceleration whose modulus depends on the velocity of the particle as \(a\sqrt v \), where a is a positive constant. At the initial moment its velocity is equal to \({v_0}\). The time it takes before it comes to rest is

Answers Choices:

\(2\frac{{\sqrt {{v_0}} }}{a}\)

\(\frac{{\sqrt {{v_0}} }}{a}\)

\(\frac{{{v_0}}}{a}\)

\(\frac{a}{{\sqrt {{v_0}} }}\)

Questions 3 of 50

Question:The law of motion of a particle moving in a straight line is given by \(s = \frac{1}{2}vt\), where v is the velocity at time t and s is the distance covered. Then acceleration is

Answers Choices:

A function of t

A function of s

A function of v

Constant

Questions 4 of 50

Question:If the displacement of a particle varies with time as \(\sqrt x = t + 7\), then

Answers Choices:

The velocity of the particle is inversely proportional to t

The velocity of the particle is proportional to t

The velocity of the particle is proportional to \(\sqrt t \)

The particle moves with a constant acceleration

2 and 4 are correct

Questions 5 of 50

Question:If OP makes 4 revolutions in one second, the angular velocity in radians per second is

Answers Choices:

\(\pi \)

\(2\pi \)

\(4\pi \)

\(8\pi \)

Questions 6 of 50

Question:A velocity \(\frac{1}{4}m/s\) is resolved into two components along OA and OB making angles \({30^o}\) and \({45^o}\) respectively with the given velocity, then the component along OB is

Answers Choices:

\(\frac{1}{8}(\sqrt 6 - \sqrt 2 )\,m/s\)

\(\frac{1}{4}(\sqrt 3 - 1)m/s\)

\(\frac{1}{4}m/s\)

\(\frac{1}{8}m/s\)

Questions 7 of 50

Question:Two straight railways converge to a level crossing at an angle \(\alpha \) and two trains are moving towards the crossing with velocities u and v. If a and b are the initial distances of the trains from the crossing, the least distance between them will be after time t given by

Answers Choices:

\(\frac{{(au + bv) + (av + bu)\cos \alpha }}{{{u^2} + {v^2} + 2uv\cos \alpha }}\)

\(\frac{{(au + bv) - (av + bu)\cos \alpha }}{{{u^2} + {v^2} - 2uv\cos \alpha }}\)

\(\frac{{(au + bv) - (av + bu)\cos \alpha }}{{{u^2} + {v^2} + 2uv\cos \alpha }}\)

None of these

Questions 8 of 50

Question:A particles moves from rest, away from a fixed point O, with an acceleration \(\frac{\mu }{{{x^2}}}\), where x is the distance of the particle from O. If it is at rest, then its distance from O is b. The velocity when it is at a distance 2b from O is

Answers Choices:

\(\frac{\mu }{b}\)

\(\frac{\mu }{{{b^2}}}\)

\(\sqrt {\frac{\mu }{{{b^2}}}} \)

\(\sqrt {\frac{\mu }{b}} \)

Questions 9 of 50

Question:If a particle A is moving along a straight line with velocity 3 m/sec and another particle B has a velocity 5 m/sec. at an angle of 60o to the path of A, then the velocity B relative to A

Answers Choices:

\(\sqrt {39} \,m/\sec \)

\(\sqrt {19} \,m/\sec \)

\(19\,m/\sec \)

None of these

Questions 10 of 50

Question:A train A is moving towards east with a velocity of 30 km/h and another train B is moving on parallel lines towards west with a speed of 40 km/h. The velocity of train A relative to train B is

Answers Choices:

10 km/h

70 km/h towards east

70 km/h towards west

None of these

Questions 11 of 50

Question:A car is travelling at a velocity of 10 km/h on a straight road. The driver of the car throws a parcel with a velocity of \(10\sqrt 2 \,km/hr\) when the car is passing by a man standing on the side of the road. If the parcel is to reach the man, the direction of throw makes the following angle with the direction of the car

Answers Choices:

\({135^o}\)

\({45^o}\)

\({\tan ^{ - 1}}(\sqrt 2 )\)

\({\tan ^{ - 1}}(1/\sqrt 2 )\)

Questions 12 of 50

Question:A man wishes to cross a river to an exactly opposite point on the other bank, if he can swim with twice the velocity of the current, then the inclination to the current of the direction in which he should swim is

Answers Choices:

\({90^o}\)

\({120^o}\)

\({150^o}\)

None of these

Questions 13 of 50

Question:A ship is moving with velocity 12 km/hr in east direction and another ship is moving with velocity 16 km/hr in north direction. The relative velocity of second ship with respect to first ship will be

Answers Choices:

20 km/hr

22 km/hr

18 km/h

\(20\sqrt 2 \) km/h

Questions 14 of 50

Question:A 30 m wide canal is flowing at the rate of 20 m/min. A man can swim at the rate of 25 m/min. in still water. The time taken by him to cross the canal perpendicular to the flow is

Answers Choices:

1.0 min

1.5 min.

2.0 min.

2.5 min.

Questions 15 of 50

Question:A man crosses a 320 m wide river perpendicular to the current in 4 minutes. If in still water he can swim with a speed 5/3 times that of the current, then the speed of the current in m/min is

Answers Choices:

30

40

50

60

Questions 16 of 50

Question:A body starts from rest with a uniform acceleration of \(8m/{\sec ^2}\). Then the time it will take in traversing the second metre of its journey is

Answers Choices:

\(\sqrt 2 \) sec

\(\frac{1}{2}\) sec

\(\left( {\frac{{\sqrt 2 - 1}}{2}} \right)\) sec

\(\left( {\frac{{\sqrt 2 + 1}}{{\sqrt 2 }}} \right)\) sec

Questions 17 of 50

Question:A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered in nth sec to the distance covered in n seconds is

Answers Choices:

\(\frac{2}{n} - \frac{1}{{{n^2}}}\)

\(\frac{1}{{{n^2}}} - \frac{1}{n}\)

\(\frac{2}{{{n^2}}} - \frac{1}{n}\)

\(\frac{2}{n} + \frac{1}{{{n^2}}}\)

Questions 18 of 50

Question:If a particle moves in a straight line with uniform acceleration, the distance traversed by it in consecutive seconds are in

Answers Choices:

A.P.

G.P.

H.P.

None of these

Questions 19 of 50

Question:A bullet moving at 100 m/sec is fired into a wood-block in which it penetrates 50 cm. If the same bullet moving with the same velocity were fired into a similar piece of wood but only 12.5 cm thick, then the velocity with which it emerges is

Answers Choices:

500 m/sec

\(\frac{{500}}{{\sqrt 3 }}m/\sec \)

\(500\sqrt 3 m/\sec \)

None of these

Questions 20 of 50

Question:A body traversed half the distance with velocity \({v_0}\). The remaining part of the distance was covered with velocity \({v_1}\) for half the time and with velocity \({v_2}\) for the other half of the time. The mean velocity of the body averaged over the whole time of motion is

Answers Choices:

\({15^o}\)

\(\frac{{2{v_0} + {v_1} + {v_2}}}{4}\)

\(\frac{{2{v_0}({v_1} + {v_2})}}{{2{v_0} + {v_1} + {v_2}}}\)

\(\frac{{{v_0}({v_1} + {v_2})}}{{{v_0} + {v_1} + {v_2}}}\)

Questions 21 of 50

Question:Two points move in the same straight line starting at the same moment from the same point in the same direction. The first moves with constant velocity u and the second starts from rest with constant acceleration f. The distance between the two points will be maximum at time

Answers Choices:

\(t = \frac{{2u}}{f}\)

\(t = \frac{u}{f}\)

\(t = \frac{u}{{2f}}\)

\(t = \frac{{{u^2}}}{f}\)

Questions 22 of 50

Question:A train starts from rest from a station with constant acceleration for 2 minutes and attains a constant speed. It then runs for 11 minutes at this speed and retards uniformly during the next 3 minutes and stops at the next station which is 9 km off. The maximum speed (in km/hr) attained by the train is

Answers Choices:

30

35

40

45

Questions 23 of 50

Question:A particle is projected from the top of tower 5 m high and at the same moment another particle is projected upward from the bottom of the tower with a speed of 10 m/s, meet at distance 'h' from the top of tower, then h

Answers Choices:

1.25 m

2.5 m

3 m

None of these

Questions 24 of 50

Question:If a body is projected vertically upwards with velocity u and t seconds afterwards another body is similarly projected with the same velocity, then the two bodies will meet after T seconds of the projection of the second body, where T =

Answers Choices:

\(\frac{{u - gt}}{{2g}}\)

\(\frac{{u - 2gt}}{{2g}}\)

\(\frac{{2u - gt}}{g}\)

\(\frac{{2u - gt}}{{2g}}\)

Questions 25 of 50

Question:A stone falling from the top of a vertical tower described m metres, when another is let fall from a point n metres below the top. If the two stones fall from rest and reach the ground together, then the time taken by them to reach the ground is

Answers Choices:

\(\frac{{n + m}}{{\sqrt {2gm} }}\)

\(\frac{{n + m}}{{\sqrt {2gn} }}\)

\(\frac{{n - m}}{{\sqrt {2gm} }}\)

\(\frac{{m - n}}{{\sqrt {2gn} }}\)

Questions 26 of 50

Question:Let \({g_1}\,m/{\sec ^2}\), \({g_2}\,m/{\sec ^2}\) be the accelerations due to gravity at two places P and Q. If a particle occupies n seconds less and acquires a velocity of m metre/sec more at place P than place Q in falling through the same distance, then m/n equals

Answers Choices:

\({g_1}{g_2}\)

\(\sqrt {\frac{{{g_1}}}{{{g_2}}}} \)

\(\sqrt {\frac{{{g_2}}}{{{g_1}}}} \)

\(\sqrt {{g_1}{g_2}} \)

Questions 27 of 50

Question:A train whose mass is 16 metric tons, moves at the rate of 72 km/hr. After applying breaks it stops in 500 metre. What is the force exerted by breaks obtaining it to be uniform

Answers Choices:

800 N

1600 N

3200 N

6400 N

Questions 28 of 50

Question:A mass of 8 kg is rolled a grass with a velocity of 28 m/sec. If the resistance be \({\left( {\frac{1}{{10}}} \right)^{th}}\) of the weight, then the body comes to rest after travelling

Answers Choices:

200 m

400 m

600 m

800 m

Questions 29 of 50

Question:If a force \({F_1}\) acts on a mass of 10 kg and in one-fifth of a second produces in it a velocity of 2 m/sec and the other force \({F_2}\) acting on a mass of 625 kg in a minute produces in it a velocity of 18 km/hr, then \({F_1}:{F_2}\)

Answers Choices:

24:25:00

48:25:00

24:05:00

48 : 125

Questions 30 of 50

Question:In a diving competition, the boards fixed at a height of 10 m above the water level. A competitor jumps from the board and dives to a depth of 5 m. If the mass of the competitor is 60 kg, then the resistance offered by the water is

Answers Choices:

588 N

1176 N

1764 N

None of these

Questions 31 of 50

Question:A particle slide down a rough inclined plane whose inclination to the horizontal is \({45^o}\) and whose coefficient of friction is 3/4. The time of descending the distance \(\frac{{4\sqrt 8 }}{5}\) m down the plane is

Answers Choices:

0.8 sec

1.2 sec

1.4 sec

1.62 sec

Questions 32 of 50

Question:A particle of mass m falls from rest at a height of 16 m and is brought to rest by penetrating \(\frac{1}{6}m\) into the ground. If the average vertical thrust exerted by the ground be 388 kg. wt, then the mass of the particle is

Answers Choices:

2 kg

\(3kg\)

\(4kg\)

\(8kg\)

Questions 33 of 50

Question:A pulley carrying a total load W hangs in a loop of a chord which passes over two fixed pulleys and has unequal weights P and Q freely suspended from the ends, each segment of the chord vertical. If W remains at rest, then W =

Answers Choices:

\(\frac{{PQ}}{{P + Q}}\)

\(\frac{{2PQ}}{{P + Q}}\)

\(\frac{{3PQ}}{{P + Q}}\)

\(\frac{{4PQ}}{{P + Q}}\)

Questions 34 of 50

Question:Two particles of masses \({m_1}\) and \({m_2}\) are connected by a light inextensible string \({m_2}\) is placed on a smooth horizontal table and the string passes over a light pulley at the edge of the table and \({m_1}\) is hanging freely. If \({m_1}\) is replaced by \({m_2}\) and \({m_2}\) is replaced by \({m_3}\), then the acceleration of the system remains unaltered if \({m_1},\,{m_2},\,{m_3}\) are in

Answers Choices:

A.P.

G.P.

H.P.

None of these

Questions 35 of 50

Question:An elastic ball with coefficient of elasticity 1/2 is dropped from rest at a height h on a smooth floor. The total distance covered by the ball is

Answers Choices:

More than 2h

Less than 2h but more than (3/2)h

Less than (3/2)h but more that (4/3)h

Less then (4/3)h

Questions 36 of 50

Question:Hailstorm are observed to strike the surface of a frozen lake in a direction making an angle of \({30^o}\) to the vertical and to rebound at an angle of \({60^o}\) to the vertical. Assuming the contact to be smooth, the coefficient of restitution is

Answers Choices:

1/3

2/3

\(1/\sqrt 3 \)

None of these

Questions 37 of 50

Question:Any heavy elastic ball falls from the ceiling of any room and after rebounding two times reaches the half of the height of ceiling. The coefficient of restitution is

Answers Choices:

\({(0.50)^{1/2}}\)

\({(0.50)^{1/3}}\)

\({(0.50)^{1/4}}\)

\({(0.25)^{1/2}}\)

Questions 38 of 50

Question:A ball of 1 kg moving with velocity 7 m/sec overtakes and collides with a ball of mass 2 kg moving with velocity 1 m/sec. in the same direction. If \(e = 3/4,\) the velocity of the lighter ball after impact is

Answers Choices:

120 m/sec

\(\frac{1}{2}\) m/sec

1 m/sec

0 m/sec

Questions 39 of 50

Question:A particle is projected under gravity \((g = 9.81m/{\sec ^2})\) with a velocity of \(29.43\,m/\sec \) at an elevation of  \({30^0}\). The time of flight in seconds to a height of 9.81 m are

Answers Choices:

5, 1, 5

1, 2

1, 5, 2

2, 3

Questions 40 of 50

Question:From the top of a tower of height 100 m, a ball is projected with a velocity of 10 m/sec. It takes 5 seconds to reach the ground. If \(g = 10m/{\sec ^2}\), then the angle of projection is

Answers Choices:

\({30^o}\)

\({45^o}\)

\({60^o}\)

\({90^o}\)

Questions 41 of 50

Question:A particle is projected with initial velocity u making an angle \(\alpha \) with the horizontal, its time of flight will be given by

Answers Choices:

\(\frac{{2u\sin \alpha }}{g}\)

\(\frac{{2{u^2}\sin \alpha }}{g}\)

\(\frac{{u\sin \alpha }}{g}\)

\(\frac{{{u^2}\sin \alpha }}{g}\)

Questions 42 of 50

Question:The escape velocity for a body projected vertically upwards is 11.2 km/sec. If the body is projected in a direction making an angle of \({60^o}\) with the vertical, then the escape velocity will be

Answers Choices:

11.2 km/sec

\(5.6\sqrt 3 km/\sec \)

5.6 km/sec

None of these

Questions 43 of 50

Question:A particle is projected up a smooth inclined plane of inclination \({60^o}\) along the line of greatest slope. If it comes to instantaneous rest after 2 second then the velocity of projection is \((g = 9.8m/{\sec ^2})\)

Answers Choices:

9.8 m/s

10 m/s

16.97 m/s

19.6 m/s

Questions 44 of 50

Question:A body is projected through an angle \(\alpha \) from vertical so that its range is half of maximum range, \(\alpha \) is

Answers Choices:

\({60^o}\)

\({75^o}\)

\(\frac{{2WW'}}{{W + W'}}\)

\({22.5^o}\)

Questions 45 of 50

Question:The angular elevation of an enemy's position on a hill h feet high is \(\beta \). Show that is order to shell if the initial velocity of the projectile must not be less than

Answers Choices:

\({[gh(1 + \sin \beta )]^{1/2}}\)

\({[gh(1 - \sin \beta )]^{1/2}}\)

\({[gh(1 + {\rm{cosec }}\beta )]^{1/2}}\)

\({[gh(1 - {\rm{c}}o\sec \beta )]^{1/2}}\)

Questions 46 of 50

Question:The ratio of the greatest range up an inclined plane through the point of projection and the distance through which a particle falls freely during the corresponding time of flight is

Answers Choices:

2

\(\frac{1}{2}\)

1

3

Questions 47 of 50

Question:A ball weighing 0.01 kg hits a hard surface vertically with a speed of 5 m/sec and rebounds with the same speed. The ball reamins in contact with the surface for 0.01 sec. The average force exerted by the surface on the ball (in Newton) is

Answers Choices:

0.1

1

5

10

Questions 48 of 50

Question:A labour has to throw bricks near mistry 16 feet vertically above. He throws the bricks in such a manner that the brick reach the mistry with the velocity of 16 ft/sec. If the throws bricks such that bricks just reach the mistry, then the portion of the energy saved is

Answers Choices:

1/3

1/4

1/5

1/6

Questions 49 of 50

Question:A hammer of mass 2 kg falls vertically through 1 metre on the top of a nail of mass 100 gm and drives it a distance of 10 cm in the ground. The resistance of the ground is

Answers Choices:

3441/210 kg wt

4441/210 kg wt

5441/210 kg wt

None of these

Questions 50 of 50

Question:A bullet of mass m penetrates a thickness a of a plate of mass M at rest. If this plate is free to move, then the thickness to which the bullet will penetrate is

Answers Choices:

\(Ma/(m + M)\)

\(ma/(m + M)\)

\((M - m)\,a/(m + M)\)

None of these