# Dyanamics Questions

Total Questions:50 Total Time: 60 Min

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## Questions 1 of 50

Question:If a particle, moving in a straight line, covers a distance s in time t, given by the relations $${s^2} = a{t^2} + 2bt + c$$, then its acceleration is

$$\frac{{{b^2} - ac}}{{{s^3}}}$$

$$\frac{{ac - {b^2}}}{{{s^3}}}$$

$$\frac{{ac - {b^2}}}{{{s^2}}}$$

$$\frac{{ac - {b^2}}}{s}$$

## Questions 2 of 50

Question:The speed v of a body moving on a straight track varies according to $$v = \left\{ {\begin{array}{*{20}{c}} {2t + 13} & , & {0 \le t \le 5} \\ {3t + 8} & , & {5 < t \le 7} \\ {4t + 1} & , & {t > 7} \\\end{array}} \right.$$. The distances are measured in metres and time t in seconds. The distance in metres moved by the particle at the end of 10 seconds is

127

247

186

313

## Questions 3 of 50

Question:If the velocity of a particle moving in a straight line is given by $${v^2} = s{e^s}$$, then its acceleration is

$$\frac{{{v^2}}}{{2s}}$$

$$\frac{{{v^2}}}{{2s}}(s + 1)$$

$$\frac{{{v^2}}}{2}(s - 1)$$

$$\frac{v}{2}(s + 1)$$

## Questions 4 of 50

Question:The position at any time t, of a particle moving along x-axis is given by the relation $$s = {t^3} - 9{t^2} + 24t + 6$$, where s denotes the distance in metre from the origin. The velocity v of the particle at the instant when the acceleration becomes zero, is given by

$$v = 3$$

$$v = - 3$$

$$v = 0$$

$$v = - 6$$

## Questions 5 of 50

Question:For a particle moving in a straight line, if time t be regarded as a function of velocity v, then the rate of change of the acceleration a is given by

$${a^2}\frac{{{d^2}t}}{{d{v^2}}}$$

$${a^3}\frac{{{d^2}t}}{{d{v^2}}}$$

$$- {a^3}\frac{{{d^2}t}}{{d{v^2}}}$$

None of these

## Questions 6 of 50

Question:If two velocities u and v are inclined at such an angle that the resultant of 2u and v inclined at the same angle is at right angle to v, then the resultant of u and v is of magnitude

2u

v

2v

u

## Questions 7 of 50

Question:If a particle having simultaneous velocities 3 m/sec., 5 m/sec. and 7 m/sec. at rest, then the angle between the first two velocities is

$${120^o}$$

$${150^o}$$

$${60^o}$$

$${90^o}$$

## Questions 8 of 50

Question:The greatest and least magnitudes of the resultants of two velocities of constant magnitudes are u and v respectively. If a particle has these velocities inclined at an angle $$2\alpha$$, then the resultant velocity is of magnitude

$${60^o}$$

$$\sqrt {{u^2}{{\sin }^2}\alpha + {v^2}{{\cos }^2}\alpha }$$

$$\sqrt {{u^2}\cos \alpha + {v^2}\sin \alpha }$$

None of these

## Questions 9 of 50

Question:A particle possesses simultaneously two velocities 10 m/sec. and 15 m/sec. in directions inclined at an angle of $$\frac{{M + m}}{{Mu}} = \frac{{M + m}}{{mu}}$$ , then its resultant velocity is

15 m/sec.

$$5\sqrt {19} \,m/\sec$$

25 m/sec

None of these

## Questions 10 of 50

Question:The average speed of a bicycle over a journey of 20 km; if it travels the first 10 km. at 15 km/hr and the second 10 km. at 10 km/hr, is

12 km/hr

10 km/hr

15 km/hr

None of these

## Questions 11 of 50

Question:Two scooterists P and Q are moving due north at 48 km/hr and 36 km/hr respectively. The velocity of P relative to Q is

12 km/hr due south

12 km/hr due north

84 km/hr due south

84 km/hr due north

## Questions 12 of 50

Question:If two particles, A and B, moves with speed u and 2u respectively in two straight lines inclined at an angle $$\alpha$$, then the relative velocity of B with respect to A is

$$u\sqrt {5 + 4\cos \alpha }$$

$$u\sqrt {5 - 4\cos \alpha }$$

$$u\sqrt {4 - 5\cos \alpha }$$

$$u\sqrt {4 + 5\cos \alpha }$$

## Questions 13 of 50

Question:A railway train, moving at the rate of 44 m/sec, is struck by a stone, moving horizontally and at right angles to the train with velocity of 33 m/sec. The magnitude and direction of the velocity with which the stone appears to meet the train is

$$50,\,{\tan ^{ - 1}}\frac{3}{4}$$

$$55,\,{\tan ^{ - 1}}\left( {\frac{{ - 3}}{4}} right)$$

$$40,\,{\cos ^{ - 1}}\frac{3}{4}$$

None of these

## Questions 14 of 50

Question:To a boy cycling at the rate of 4 km/hr eastward, the wind seems to blow directly, from the north. But when he cycles at the rate of 7 km/hr, it seems to blow from north-east. The magnitude of the actual velocity of the wind is

$$5/\sqrt 2 km/hr$$

$$5\sqrt 2 \,km/hr$$

$$5km/hr$$

$$5\frac{1}{2}km/hr$$

## Questions 15 of 50

Question:A boat takes 10 minutes to cross a river in a straight line from a point A on the bank to a point B on the other bank and 20 minutes to do the return journey. The current flows at the rate of 3 km/hr and the speed of the boat relative to the water is 6 km/hr. The width of the river and the down stream distance from A to B are

$$m/\sec .$$

$$\frac{{\sqrt {10} }}{4},\,\frac{1}{3}$$

$$\sqrt 6 ,\,\frac{1}{2}$$

None of these

## Questions 16 of 50

Question:If a moving particle has two equal velocities inclined at an angle $$2\alpha$$ such that their resultant velocity is twice as great as when they are inclined at an angle $$2\beta$$, then

$$\cos \alpha = 2\cos \beta$$

$$\cos \beta = 2\cos \alpha$$

$$\cos \alpha = 3\cos \beta$$

$$\cos \beta = 3\cos \alpha$$

## Questions 17 of 50

Question:The speed of a boat in a river is u m/sec and that of the current is v $$m/\sec .$$ The boat traverse a distance of d metres down the stream and then comes back to its original position. The average speed of the boat for to and fro journey is

$$\frac{{{u^2} - {v^2}}}{{{u^2}}}$$

$$\frac{{{u^2} - {v^2}}}{{{v^2}}}$$

$$\frac{{{u^2} - {v^2}}}{u}$$

$$\frac{{{u^2} - {v^2}}}{v}$$

## Questions 18 of 50

Question:A thief, when detected, jumps out of a running train at right angles to its direction with a velocity of 5 m/min. If the velocity of the train is 36 km/hr, then the angle $$(f + g)$$ between the direction in which the thief falls and the direction of motion of the train is given by

$${\tan ^{ - 1}}\left( {\frac{5}{{36}}} \right)$$

$${\tan ^{ - 1}}\left( {\frac{1}{{120}}} \right)$$

$${\tan ^{ - 1}}\left( {\frac{5}{{120}}} \right)$$

None of these

## Questions 19 of 50

Question:A person travelling on a straight line moves with uniform velocity $${v_1}$$ for some time and with uniform velocity $${v_2}$$ for the next equal time. The average velocity 'v' is given by

$$v = \frac{{{v_1} + {v_2}}}{2}$$

$$v = \sqrt {{v_1}{v_2}}$$

$$\frac{2}{v} = \frac{1}{{{v_1}}} + \frac{1}{{{v_2}}}$$

$$\frac{1}{v} = \frac{1}{{{v_1}}} + \frac{1}{{{v_2}}}$$

## Questions 20 of 50

Question:A particle starts with a velocity of 200 cm/sec and moves in a straight line with a retardation of 10 cm/sec2. Then the time it takes to describe 1500 cm is

10 sec, 30 sec

5 sec, 15 sec.

10 sec

30 sec

## Questions 21 of 50

Question:For $$\frac{1}{m}$$ of the distance between two stations a train is uniformly accelerated and $$\frac{1}{n}$$ of the distance it is uniformly retarded, it starts from rest at one station and comes to rest at the other. Then the ratio of its greatest velocity to its average velocity is

$$m + n + 1:1$$

$$\left( {\frac{1}{m} + \frac{1}{n}} \right)\,:\,1$$

$$\frac{1}{m} + \frac{1}{n} + 1:1$$

$$m + n + 1:mn$$

## Questions 22 of 50

Question:A train starts from station A with uniform acceleration $${f_1}$$ for some distance and then goes with uniform retardation $${f_2}$$ for some more distance to come to rest at B. If the distance between stations A and B is 4 km and the train takes 4 minutes to complete this journey, then $$\frac{1}{{{f_1}}} + \frac{1}{{{f_2}}} =$$

1

2

4

None of these

## Questions 23 of 50

Question:Two bodies of different masses $${m_1}$$ and $${m_2}$$ are dropped from different heights $${h_1}$$ and $${h_2}$$. The ratio of the times taken by the two bodies to fall through these distances is

$${h_1}:{h_2}$$

$$\sqrt {{h_1}} :\sqrt {{h_2}}$$

$$h_1^2:h_2^2$$

$${h_2}:{h_1}$$

## Questions 24 of 50

Question:The time to slide down the chord through the highest point of a vertical circle is

Variable

Constant

Dependent on the position of the chord

None of these

## Questions 25 of 50

Question:Two particles A and B are dropped from the height of 5 m and 20 m respectively. Then the ratio of time taken by A to that taken by B, to reach the ground is

1:4

2:1

1:2

1:1

## Questions 26 of 50

Question:A body is projected upwards with a certain velocity , and it is found that when in its ascent, it is 29430 cm from the ground it takes 4 seconds to return to the same point, again. The velocity of projection of the body is

7000 cm/sec

7848 cm/sec

8000 cm/sec

None of these

## Questions 27 of 50

Question:A dyne is the force which produces an acceleration of $$1cm/{\sec ^2}$$ when acted on a mass of

$$1\,mg$$

$$1gm$$

$$10gm$$

$$1kg$$

## Questions 28 of 50

Question:A balloon of mass m ascends with a uniform acceleration f. If a certain part of the balloon is detached in such a way that the acceleration is doubled, then the mass of the detached portion is

$$\frac{{fm}}{{f + g}}$$

$$\frac{{fm}}{{f + 2g}}$$

$$\frac{{fm}}{{2f + g}}$$

$$\frac{{gm}}{{2f + g}}$$

## Questions 29 of 50

Question:In a rectilinear motion a particle of mass m changes its velocity from u to v in describing a distance x. If F is the constant force which produces the changes, then $$F =$$

$$\frac{1}{2}m({v^2} - {u^2})$$

$$\frac{1}{{2x}}m({v^2} - {u^2})$$

$$\frac{1}{{2x}}m({v^2} + {u^2})$$

None of these

## Questions 30 of 50

Question:A cricket ball of mass 200 gm moving with a velocity of 20 m/sec is brought to rest by a player in 0.1 sec. The average force applied by the player is

$$4 \times {10^3}dynes$$

$$4 \times {10^4}dynes$$

$$4 \times {10^5}dynes$$

$$4 \times {10^6}dynes$$

## Questions 31 of 50

Question:From the gun cartage of mass M, a fire arm of mass m with velocity u relative to gun cartage is fired. The real velocities of fire arms and gun cartage will be respectively

$$\frac{{Mu}}{{M + m}},\;\frac{{Mu}}{{M - u}}$$

$$\frac{{Mu}}{{M + m}},\;\frac{{mu}}{{M + m}}$$

$$\frac{{M + m}}{{Mu}},\;\frac{{M + m}}{{mu}}$$

$$\frac{{M + m}}{{M - m}},\;\frac{{M + m}}{{Mm}}$$

## Questions 32 of 50

Question:The shortest time from rest to rest in which a steady load of P tons can lift a weight of W tons through a vertical distance h feet is

$$\sqrt {\left( {\frac{{2h}}{g}.\frac{P}{{P - W}}} \right)}$$

$$\sqrt {\left( {\frac{{2h}}{g}.\frac{P}{{P + W}}} \right)}$$

$$\sqrt {\left( {\frac{{2h}}{g}.\frac{{P + W}}{{P - W}}} \right)}$$

None of these

## Questions 33 of 50

Question:A shot, whose mass is 400 kg, is discharged from a 80 metric ton gun with a velocity of 490 m/sec. The necessary force required to stop the gun after a recoil of 1.6 m is

245/16 metric ton

15 metric ton

20 metric ton

None of these

## Questions 34 of 50

Question:A rough plane is 100 ft long and is inclined to the horizon at an angle $${\sin ^{ - 1}}(3/5)$$, the coefficient of friction being 1/2, and a body slides down it from rest at the highest point, the velocity on reaching the bottom would be

$$16/\sqrt 5$$ ft/sec

$$16\,ft/\sec$$

$$16\sqrt 5 ft/\sec$$

$$16/\sqrt 7 ft/\sec .$$

## Questions 35 of 50

Question:A mass of 6 kg slides down a smooth inclined plane whose height is half its length, and draws another mass from rest over a distance 3 m in 5 sec along a smooth horizontal table which is level with the top of the plane over which the string passes, the mass on the table is

86.5 kg

96.5 kg

106.5 kg

116.5 kg

## Questions 36 of 50

Question:Two equal perfectly elastic balls impinges directly, then after impact they

Are at rest

Interchange their velocities

Move with the same velocities

Move with twice velocities

## Questions 37 of 50

Question:A sphere impinges directly on an equal sphere at rest. If the coefficient of restitution is e, their velocities after the impact are as

1 : e

$$e:1$$

$$1 + e:1 - e$$

$$1 - e:1 + e$$

## Questions 38 of 50

Question:A ball is dropped from a height of 22.5 metre on a fixed horizontal plane. If $$e = 2/5$$, then it will stop rebounding after

5 sec.

6 sec.

7 sec.

8 sec.

## Questions 39 of 50

Question:A particle is thrown over a triangle from one end of horizontal base. If $$\alpha ,\,\beta$$ are the base angles and $$\theta$$ the angle of projection, then

$$\tan \theta = \tan \alpha - \tan \beta$$

$$\tan \theta = \tan \beta - \tan \alpha$$

$$\tan \theta = \tan \alpha + \tan \beta$$

None of these

## Questions 40 of 50

Question:A particle is projected down an inclined plane with a velocity of 21 m/sec at an angle of $${60^o}$$ with the horizontal. Its range on the inclined plane, inclined at an angle of $${30^o}$$ with the horizontal is

21 dm

2.1 dm

30 dm

6 dm

## Questions 41 of 50

Question:If you want to kick a football to the maximum distance the angle at which it should be kicked is (assuming no resistance)

$${45^o}$$

$${90^o}$$

$${30^o}$$

$${60^o}$$

## Questions 42 of 50

Question:The path of projectile in vacuum is a

Straight line

Circle

Ellipse

Parabola

## Questions 43 of 50

Question:If a projectile having horizontal range of 24 acquires a maximum height of 8, then its initial velocity and the angle of projection are

$$24\sqrt g ,\,{\sin ^{ - 1}}(0.6)$$

$$8\sqrt g ,\,{\sin ^{ - 1}}(0.8)$$

$$5\sqrt g ,{\sin ^{ - 1}}(0.8)$$

$$5\sqrt g ,\,{\sin ^{ - 1}}(0.6)$$

## Questions 44 of 50

Question:The range of a projectile fixed at an angle of $${15^o}$$ is 50 m, if it is fixed with the same speed at an angle of $${45^o}$$, then the range will be

50 m

100 m

150 m

None of these

## Questions 45 of 50

Question:A particle is projected from a point O with velocity u at an angle of  $${60^0}$$ with the horizontal. When it is moving in a direction at right angles to its direction at O, its velocity then is given by

$$\frac{{2u}}{3}$$

$$\frac{u}{{\sqrt 3 }}$$

$$\frac{u}{3}$$

$$\frac{u}{2}$$

## Questions 46 of 50

Question:AB is the vertical diameter of a circle in a vertical plane. Another diameter CD makes an angle of $${60^o}$$ with AB, then the ratio of the time taken by a particle to slide along AB to the time taken by it to slide along CD is

1:01

$$\sqrt 2 :1$$

$$1:\sqrt 2$$

$${3^{1/4}}:{2^{1/2}}$$

## Questions 47 of 50

Question:A body is 3 kg is projected upwards with such a velocity that it can reach the height 196 metres only. The kinetic energy of the body at the time of projection is

5000 Joule

5762.4 Joule

6000 Joule

None of these

## Questions 48 of 50

Question:A bullet of 125 grams strikes a target with a velocity of 400 metres per second and is embedded in it. If the target weighs 10 kg and is free to move, then the velocity of the target after impact is

400/81 m/sec

400 m/sec

300 m/sec

None of these

## Questions 49 of 50

Question:A bullet is shot with a velocity of 600 m/sec into a target weighing 12 kg and is free to move with a velocity 1.5 m/sec after impact. Then the percentage loss of kinetic energy in the impact is

79.75%

89.75%

99.75%

None of these

## Questions 50 of 50

Question:A 15 kg block is moving on ice with a speed of 5 metre per second when a 10 kg block is dropped onto it vertically. The two together move with a velocity which in metre per second is

$$\sqrt {(15)}$$