Total Questions:50 Total Time: 60 Min
Remaining:
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
\(\frac{{{b^2} - ac}}{{{s^3}}}\)
\(\frac{{ac - {b^2}}}{{{s^3}}}\)
\(\frac{{ac - {b^2}}}{{{s^2}}}\)
\(\frac{{ac - {b^2}}}{s}\)
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
Question:If the velocity of a particle moving in a straight line is given by \({v^2} = s{e^s}\), then its acceleration is
\(\frac{{{v^2}}}{{2s}}\)
\(\frac{{{v^2}}}{{2s}}(s + 1)\)
\(\frac{{{v^2}}}{2}(s - 1)\)
\(\frac{v}{2}(s + 1)\)
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
\(v = 3\)
\(v = - 3\)
\(v = 0\)
\(v = - 6\)
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
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
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
\({120^o}\)
\({150^o}\)
\({60^o}\)
\({90^o}\)
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
\(\sqrt {{u^2}{{\sin }^2}\alpha + {v^2}{{\cos }^2}\alpha } \)
\(\sqrt {{u^2}\cos \alpha + {v^2}\sin \alpha } \)
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
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
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
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
\(u\sqrt {5 + 4\cos \alpha } \)
\(u\sqrt {5 - 4\cos \alpha } \)
\(u\sqrt {4 - 5\cos \alpha } \)
\(u\sqrt {4 + 5\cos \alpha } \)
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
\(50,\,{\tan ^{ - 1}}\frac{3}{4}\)
\(55,\,{\tan ^{ - 1}}\left( {\frac{{ - 3}}{4}} right)\)
\(40,\,{\cos ^{ - 1}}\frac{3}{4}\)
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
\(5/\sqrt 2 km/hr\)
\(5\sqrt 2 \,km/hr\)
\(5km/hr\)
\(5\frac{1}{2}km/hr\)
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
\(m/\sec .\)
\(\frac{{\sqrt {10} }}{4},\,\frac{1}{3}\)
\(\sqrt 6 ,\,\frac{1}{2}\)
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
\(\cos \alpha = 2\cos \beta \)
\(\cos \beta = 2\cos \alpha \)
\(\cos \alpha = 3\cos \beta \)
\(\cos \beta = 3\cos \alpha \)
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
\(\frac{{{u^2} - {v^2}}}{{{u^2}}}\)
\(\frac{{{u^2} - {v^2}}}{{{v^2}}}\)
\(\frac{{{u^2} - {v^2}}}{u}\)
\(\frac{{{u^2} - {v^2}}}{v}\)
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
\({\tan ^{ - 1}}\left( {\frac{5}{{36}}} \right)\)
\({\tan ^{ - 1}}\left( {\frac{1}{{120}}} \right)\)
\({\tan ^{ - 1}}\left( {\frac{5}{{120}}} \right)\)
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
\(v = \frac{{{v_1} + {v_2}}}{2}\)
\(v = \sqrt {{v_1}{v_2}} \)
\(\frac{2}{v} = \frac{1}{{{v_1}}} + \frac{1}{{{v_2}}}\)
\(\frac{1}{v} = \frac{1}{{{v_1}}} + \frac{1}{{{v_2}}}\)
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
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
\(m + n + 1:1\)
\(\left( {\frac{1}{m} + \frac{1}{n}} \right)\,:\,1\)
\(\frac{1}{m} + \frac{1}{n} + 1:1\)
\(m + n + 1:mn\)
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
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
\({h_1}:{h_2}\)
\(\sqrt {{h_1}} :\sqrt {{h_2}} \)
\(h_1^2:h_2^2\)
\({h_2}:{h_1}\)
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
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
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
Question:A dyne is the force which produces an acceleration of \(1cm/{\sec ^2}\) when acted on a mass of
\(1\,mg\)
\(1gm\)
\(10gm\)
\(1kg\)
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
\(\frac{{fm}}{{f + g}}\)
\(\frac{{fm}}{{f + 2g}}\)
\(\frac{{fm}}{{2f + g}}\)
\(\frac{{gm}}{{2f + g}}\)
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 \(F = \)
\(\frac{1}{2}m({v^2} - {u^2})\)
\(\frac{1}{{2x}}m({v^2} - {u^2})\)
\(\frac{1}{{2x}}m({v^2} + {u^2})\)
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
\(4 \times {10^3}dynes\)
\(4 \times {10^4}dynes\)
\(4 \times {10^5}dynes\)
\(4 \times {10^6}dynes\)
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
\(\frac{{Mu}}{{M + m}},\;\frac{{Mu}}{{M - u}}\)
\(\frac{{Mu}}{{M + m}},\;\frac{{mu}}{{M + m}}\)
\(\frac{{M + m}}{{Mu}},\;\frac{{M + m}}{{mu}}\)
\(\frac{{M + m}}{{M - m}},\;\frac{{M + m}}{{Mm}}\)
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
\(\sqrt {\left( {\frac{{2h}}{g}.\frac{P}{{P - W}}} \right)} \)
\(\sqrt {\left( {\frac{{2h}}{g}.\frac{P}{{P + W}}} \right)} \)
\(\sqrt {\left( {\frac{{2h}}{g}.\frac{{P + W}}{{P - W}}} \right)} \)
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
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
\(16\,ft/\sec \)
\(16\sqrt 5 ft/\sec \)
\(16/\sqrt 7 ft/\sec .\)
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
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
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
\(e:1\)
\(1 + e:1 - e\)
\(1 - e:1 + e\)
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.
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
\(\tan \theta = \tan \alpha - \tan \beta \)
\(\tan \theta = \tan \beta - \tan \alpha \)
\(\tan \theta = \tan \alpha + \tan \beta \)
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
Question:If you want to kick a football to the maximum distance the angle at which it should be kicked is (assuming no resistance)
\({45^o}\)
\({30^o}\)
Question:The path of projectile in vacuum is a
Straight line
Circle
Ellipse
Parabola
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
\(24\sqrt g ,\,{\sin ^{ - 1}}(0.6)\)
\(8\sqrt g ,\,{\sin ^{ - 1}}(0.8)\)
\(5\sqrt g ,{\sin ^{ - 1}}(0.8)\)
\(5\sqrt g ,\,{\sin ^{ - 1}}(0.6)\)
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
Question:A particle is projected from a point O with velocity u at an angle ofÂ \({60^0}\) with the horizontal. When it is moving in a direction at right angles to its direction at O, its velocity then is given by
\(\frac{{2u}}{3}\)
\(\frac{u}{{\sqrt 3 }}\)
\(\frac{u}{3}\)
\(\frac{u}{2}\)
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
\(\sqrt 2 :1\)
\(1:\sqrt 2 \)
\({3^{1/4}}:{2^{1/2}}\)
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
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
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%
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
3
\(\sqrt {(15)} \)
5
Indeterminate