# Dynamics Questions Test 3

Total Questions:50 Total Time: 60 Min

Remaining:

## Questions 1 of 50

Question:The x and y displacement of a particle in the xy-plane at any instant are given by $$x = a{t^2}$$ and $$y = 2at$$, where a is a constant. The velocity of the particle at any instant is given by

$$4a\sqrt {{t^2} + 4}$$

$$2a\sqrt {{t^2} + 1}$$

$$4a\sqrt {{t^2} + 1}$$

$$\frac{a}{2}\sqrt {{t^2} + 4}$$

## Questions 2 of 50

Question:The acceleration of a particle, starting from rest, varies with time according to the relation $$a = - s{\omega ^2}\sin \omega t$$. The displacement of this particle at time t will be

$$s\,\sin \omega t$$

$$s\omega \cos \omega t$$

$$s\omega \sin \omega t$$

$$- \frac{1}{2}(s{\omega ^2}\sin \omega t)\,{t^2}$$

## Questions 3 of 50

Question:A particle moves along a straight line in such a way that its distance from a fixed point on the line, at any time t from the start, is given by the equation $$s = 6 - 2t + 3{t^3}$$. Its acceleration after 1 second of motion is

12

16

18

None of these

## Questions 4 of 50

Question:A particle moves in a straight line with a velocity given by $$\frac{{dx}}{{dt}} = x + 1$$. The time taken by the particle to traverse a distance of 99 metres is

$${\log _{10}}e$$

$$2{\log _e}10$$

$$2{\log _{10}}e$$

$$\frac{1}{2}{\log _{10}}e$$

## Questions 5 of 50

Question:The velocity v of a particle is at any time related to the distance travelled by the particle by the relation $$v = as + b$$, where $$a > 0$$ and $$b \le a/2$$. Which of the following statements will be true for this motion (Given $$s = 0$$ when $$t = 0$$)

The displacement of the particle at time t is $$s = \frac{b}{a}({e^{at}} - 1)$$

The particle will experience a retardation if $$b > 0$$

The particle will be at rest at $${m_2}$$

The motion of the particle is under constant acceleration

## Questions 6 of 50

Question:A particle moving in a straight line is subject to a resistance which produces a retardation $$k{v^3}$$, where v is the velocity and k is a constant. If u is the initial velocity of the particle, then

$$v = \frac{u}{{1 + kxu}}$$

$$v = \frac{u}{{1 + xu}}$$

$$v = \frac{{ku}}{{1 + kxu}}$$

$$v = \frac{u}{{1 - kxu}}$$

## Questions 7 of 50

Question:A particle moves towards east from a point A to a point B at the rate of 4 km/h and then towards north from B to C at the rate of 5 km/h. If AB = 12 km and BC = 5 km, then its average speed for its journey from A to C and resultant average velocity direct from A to C are respectively

$$\frac{{13}}{9}$$km/h and [\frac{{17}}{9}\) km/h

$$\frac{{13}}{4}$$ km/h and $$\frac{{17}}{4}$$ km/h

$$\frac{{17}}{9}km/h$$ and $$\frac{{17}}{9}$$ km/h

$$\frac{{17}}{4}km/h$$ and $$\frac{{13}}{4}km/h$$

## Questions 8 of 50

Question:If a particle moves in a straight line according to the formula, $$x = {t^3} - 6{t^2} - 15t$$, then the time interval during which the velocity is negative and acceleration is positive, is

[0, 5]

$$(2,\,\infty )$$

(2, 5)

None of these

## Questions 9 of 50

Question:A man rows directly across a flowing river in time $${t_1}$$ and rows an equal distance down the stream in time $${t_2}$$. If u be the speed of the man in still water and v be that of the stream, then $${t_1}:{t_2} =$$

$$u + v:u - v$$

$$u - v:u + v$$

$$\sqrt {u + v} :\sqrt {u - v}$$

$$\sqrt {u - v} :\sqrt {u + v}$$

## Questions 10 of 50

Question:A person travelling towards the north-east, finds that the wind appears to blow from north, but when he doubles his speed it seems to come from a direction inclined at an angle $${\tan ^{ - 1}}\frac{1}{2}$$ on the east of north. The true direction of the wind is towards

North-east

North

East

None of these

## Questions 11 of 50

Question:A man is walking towards north with speed 4.5 km/hr . Another man is running towards west with speed 6 km/hr. The magnitude and direction of the relative velocity of the second with respect to first is

7.5 km/hr at an angle $${\tan ^{ - 1}}\left( {\frac{3}{4}} \right)$$ south of west

7.5 km/hr at an angle $${\tan ^{ - 1}}\left( {\frac{3}{4}} \right)$$ west of south

7.5 km/hr south-west

None of these

## Questions 12 of 50

Question:A man is swimming in a lake in a direction $${30^o}$$ east of north with a speed of 5 km/hr and a cyclist is going on the road along the lake shore towards east at a speed of 10 km/hr. The direction of the swimmer relative to the cyclist is

$${30^o}$$ west of north

West-north

$${60^o}$$ west of north

None of these

## Questions 13 of 50

Question:If a point moves with constant acceleration from A to B in the straight line AB has velocities u and v at A and B respectively, then the velocity at C, the mid-point of AB is

$$\frac{{u + v}}{2}$$

$$\sqrt {{u^2} + {v^2}}$$

$$\sqrt {\frac{{{u^2} + {v^2}}}{2}}$$

None of these

## Questions 14 of 50

Question:A point is moving with uniform acceleration, in the eleventh and fifteenth seconds from the commencement it moves through 720 and 960 cm respectively. Its initial velocity, and the acceleration with which it moves are

60, 40

70, 30

90, 60

None of these

## Questions 15 of 50

Question:A particle is moving in a straight line with initial velocity u and uniform acceleration f. If the sum of the distances travelled in tth and $${(t + 1)^{th}}$$ seconds is 100 cm, then its velocity after t seconds, in cm/sec. is

20

30

50

80

## Questions 16 of 50

Question:A point moves from rest with constant acceleration. If it covered $$\frac{9}{{25}}$$ part of its total distance in its last second of motion, then upto what time it travelled

5 second

$$9.8\sqrt 2$$ second

1 and 2 both are true

$$6\frac{1}{3}$$ second

## Questions 17 of 50

Question:Two points $$A$$ and $$B$$ move from rest along a straight line with constant acceleration $$f$$and $$f'$$ respectively. If $$A$$ takes more than $$B$$ and describes n unit more than $$B$$ in acquiring the same speed, then

$$\frac{1}{2}(f + f')m = ff'{n^2}$$

$$(f' - f)n = \frac{1}{2}ff'{m^2}$$

$$(f - f'){m^2} = ff'n$$

$$(f + f'){m^2} = ff'n$$

## Questions 18 of 50

Question:A lizard, at an initial distance of 21cm behind an insect, moves from rest with an acceleration of $$2cm/{s^2}$$ and pursues the insect which is crawling uniformly along a straight line at a speed of $$20cm/s$$. Then the lizard will catch the insect after

21sec

24 sec

20 sec

1 sec

## Questions 19 of 50

Question:If a particle is thrown vertically upwards with a velocity of u cm/sec under gravity, then the time for the particle to come to earth again is

$$\frac{u}{g}\,\sec$$

$$\frac{{2u}}{g}\sec$$

$$\frac{u}{{2g}}\sec$$

None of these

## Questions 20 of 50

Question:Two balls are projected at the same instant, from the same point with the same velocity, one vertically upwards and other vertically downwards. If first takes $${t_1}$$ sec and second takes $${t_2}$$ sec to reach the ground, then $${t_1}{t_2} =$$

$$\frac{h}{g}$$

$$2gh$$

$$\frac{{2h}}{g}$$

$$gh$$

## Questions 21 of 50

Question:If a particle is projected vertically upwards and is at a height h after $${t_1}$$ seconds and again after $${t_2}$$ seconds, then $$h =$$

$$g{t_1}{t_2}$$

$$\sqrt {g{t_1}{t_2}}$$

$$2g{t_1}{t_2}$$

$$\frac{1}{2}g{t_1}{t_2}$$

## Questions 22 of 50

Question:After a ball has been falling under gravity for 5 seconds it passes through a pane of glass and loses half of its velocity and now reaches the ground in one second. The height of the glass above the ground is

2000 m

2500 m

2943 m

None of these

## Questions 23 of 50

Question:A tower is 61.25 m high. A rigid body is dropped from its top and at the same instant another body is thrown upwards from the bottom of the tower with such a velocity that they meet in the middle of the tower. The velocity of the projection of the second body is

20 m/sec

25 m/sec

24.5 m/sec

None of these

## Questions 24 of 50

Question:A particle is dropped from the top of a tower h metres high and at the same moment another particle is projected upwards from the bottom of the tower. If the two particles meet when the upper one has described $${\left( {\frac{1}{n}} \right)^{th}}$$ of the distance, then the velocities when they meet are in the ratio

$$2:n - 2$$

$$(n - 1):2$$

$$(n + 2):2$$

$$2:n + 2$$

## Questions 25 of 50

Question:A particle was dropped from the top of the tower of height h and at the same time another particle is thrown vertically upwards form the bottom of the tower with such a velocity that it can just reach the top of the tower. The two particles meet at a height

$$\frac{h}{2}$$

$$\frac{3}{5}h$$

$$\frac{{3h}}{4}$$

$$\frac{h}{4}$$

## Questions 26 of 50

Question:A stone is dropped from an aeroplane which is rising with acceleration f and t seconds after this another stone is dropped. The distance between the two stones at time T after the second stone is dropped is

$$\frac{1}{2}(g + f)\,(t + T)\;t$$

$$\frac{1}{2}(g + f)\,(t + 2T)\;t$$

$$\frac{1}{2}(g + f)(2t + T)\;t$$

$$\frac{1}{2}(g - f)\,(t + 2T)\;t$$

## Questions 27 of 50

Question:A man weighing 60 kg jumps off a railway train running on horizontal rails at 20 km/h with a packet weighing 10 kg in his hand. The thrust of the packet on his hand is

0

10 kg wt.

50 kg wt.

70 kg wt.

## Questions 28 of 50

Question:The times of ascent and descent of a particle projected along an inclined plane of inclination $$\alpha$$ are $${t_1}$$ and $${t_2}$$ respectively, the coefficient of friction is

$$\frac{{{t_2} - {t_1}}}{{{t_2} + {t_1}}}\tan \alpha$$

$$\frac{{{t_2} + {t_1}}}{{{t_2} - {t_1}}}\tan \alpha$$

$$\frac{{t_2^2 - t_1^2}}{{t_2^2 + t_1^2}}\tan \alpha$$

$$\frac{{t_2^2 + t_1^2}}{{t_2^2 - t_1^2}}\tan \alpha$$

## Questions 29 of 50

Question:A bullet of mass 10 gram fired into a wall with a velocity of 10 m/sec loses its velocity in penetrating through 5 cm into the wall. The average force exerted by the wall is

10$$^4$$ gm wt

10$$^6$$ dynes

10$$^5$$ dynes

None of these

## Questions 30 of 50

Question:If body of mass M kg and at rest is acted upon by a constant force of W kg weight, then in seconds it moves through a distance of

$$\frac{{gTW}}{{2M}}metre$$

$$\frac{{gT{W^2}}}{{2M}}metre$$

$$\frac{{{g^2}TW}}{{2M}}metre$$

$$\frac{{g{T^2}W}}{{2M}}$$ metre

## Questions 31 of 50

Question:A train is moving with constant velocity. If the resistance of its motion is 10 lbs per ton (of mass) and the force exerted by the engine is 200 lbs wt, then the mass of engine is

20 tons

200 tons

2000 tons

2 tons

## Questions 32 of 50

Question:A light string passing over a light smooth pulley carries masses of 3 kg and 5 kg at its ends. If the string breaks after the masses have moved 9 m, then the 3 kg mass will farther rise $$(g = 10m/{\sec ^2})$$

1.75 m

1.95 m

2.05 m

2.25 m

## Questions 33 of 50

Question:A light string passing over a light smooth pulley carries masses of 3 kg and 5 kg at its ends. If the string is allowed to move from the rest, the acceleration of the motion is equal to

$$(g/2)\;m/{s^2}$$

$$(g/4)\;m/{s^2}$$

$$2g\;m/{s^2}$$

$$4g\;m/{s^2}$$

## Questions 34 of 50

Question:Two bodies of mass 8 and 10 gm is attached to a light rope which is passing over a smooth pulley. If this system is given to a velocity $$\frac{3}{{16}}$$ g cm/sec, then small body will move downwards and heavy body will move upwards, then after what time they will move in opposite directions

$$\frac{{25}}{{16}}$$sec

$$\frac{{23}}{{14}}$$sec

$$\frac{{27}}{{16}}$$sec

$$\frac{{81}}{{512}}$$sec

## Questions 35 of 50

Question:Two masses $${m_1}$$ and $${m_2}$$ are connected by a light inextensible string and suspended over a smooth fixed pulley. Then

Pressure on the pulley = $${m_1}g$$

Pressure on the pulley = $${m_2}g$$

Pressure$$< ({m_1} + {m_2})g$$

Pressure > $$({m_1} + {m_2})g$$

## Questions 36 of 50

Question:Two strings pass over a smooth pulley, on one side they are attached to masses of 3 and 4 kg respectively, and on the other to a mass of 5 kg. Then the tensions of the strings are

2, 3 kg wt.

5/2, 10/3 kg wt.

3, 4 kg wt.

None of these

## Questions 37 of 50

Question:A ball is dropped from a height of 25 dm above a fixed horizontal plane. If it rebounds to a height of 16 dm, then the coefficient of restitution is

16/25

0.8

16 g/25

0.8 g

## Questions 38 of 50

Question:A ball falls from a height h upon a fixed horizontal plane, e is the coefficient of restitution, the whole distance described by the ball before it comes to rest is

$$\frac{{1 + {e^2}}}{{1 - {e^2}}}h$$

$$\frac{{1 - {e^2}}}{{1 + {e^2}}}h$$

$$\frac{{1 + {e^2}}}{{(1 - {e^2})h}}$$

$$\frac{{1 - {e^2}}}{{(1 + {e^2})h}}$$

## Questions 39 of 50

Question:A ball is thrown from a point at a distance c from a smooth vertical wall and against the wall and returns to the point of projection. If e as the coefficient of restitution, $$\alpha$$ the angle of projection, the time of flight of the ball is

$${\left[ {\frac{{2(1 - e)c}}{{eg}}\tan \alpha } \right]^{1/2}}$$

$${\left[ {\frac{{2(1 + e)c}}{{eg}}\tan \alpha } \right]^{1/2}}$$

$$2(1 + e)\,c\tan \alpha$$

None of these

## Questions 40 of 50

Question:A ball of mass 8 kg and moving with velocity 4 m/sec collides with another ball of mass 10 kg moving with velocity 2 m/sec in the same direction. If the coefficient of restitution is 1/2, the velocities (in m/sec) of the balls after impact are

0, 0

7/3, 10/3

2/3, 5/3

2, 2

## Questions 41 of 50

Question:2A particle is projected with the speed of $$10\sqrt 5 m/\sec$$ at an angle of $${60^o}$$ from the horizontal. The velocity of the projectile when it reaches the height of 10 m is ($$g = 9.8\,m/{\sec ^2}$$)

$$4\sqrt {(19)} \,m/\sec$$

$$\sqrt {(179)} \,m/\sec$$

$$15\,m/\sec$$

$$5\sqrt {(15)} \,m/\sec$$

## Questions 42 of 50

Question:From the top of a hill of height 150 m, a ball is projected with a velocity of 10 m/sec. It takes 6 second to reach the ground. The angle of projection of the ball is

$${15^o}$$

$${30^o}$$

$${45^o}$$

$${60^o}$$

## Questions 43 of 50

Question:A cricket ball is thrown from the top of a cliff 200 m high with a velocity of 80 m/sec. at an elevation of $${30^o}$$ above the horizon, the horizontal distance from the foot of the cliff to the point where it hits the ground is (take $$g = 10m/{\sec ^2}$$)

595.3 m

695.3 m

795.3 m

895.3 m

## Questions 44 of 50

Question:A particle is projected with a velocity of 39.2 m/sec at an angle of $${30^o}$$ to the horizontal. It will move at right angle to the direction of projection after the time

8 sec

5 sec

6 sec

10 sec

## Questions 45 of 50

Question:A stone is projected so that its horizontal range is maximum and equal to 80 ft. Its time of flight and the height it rises are

$$\sqrt 3 ,\,\,1$$

$$\sqrt 4 ,\,\,15$$

$$\sqrt 5 ,\,20$$

None of these

## Questions 46 of 50

Question:The velocity and direction of projection of a shot which passes in horizontal direction just over the top of a wall which is 50 yds. away and 75 feet high

$$40,{30^o}$$

$$40\sqrt 6 ,\,{45^o}$$

$$50,\,{60^o}$$

None of these

## Questions 47 of 50

Question:A shot fired from a gun on top of a tower, 272 feet high hits the ground at a distance of 4352 feet in 17 seconds. The velocity and direction of projection are

256, $${30^o}$$

$$256\sqrt 2 ,\,{45^o}$$

$$180,\,{60^o}$$

None of these

## Questions 48 of 50

Question:If the time taken in slipping down on smooth inclined plane is twice to the time taken in falling from the vertical height of that plane, then the inclination of plane will be

$${45^o}$$

$${60^o}$$

$${75^o}$$

$${30^o}$$

## Questions 49 of 50

Question:A glass marble, whose mass is $$(1/10)kg$$ falls from a height of 2.5 m and rebounds to a height of 1.6 m. Then the average force between the marble and the floor, if the time during which they are in contact be one-tenth of a second, is

10.58 N

11.58 N

12.58 N

13.58 N

## Questions 50 of 50

Question:A fire engine lifts 50 kg water up to 2 m height per minutes and throws it out with the velocity of 19.62 m/sec. The horse power of engine will be