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Q.6 A ball collides elastically with another ball of the samemass. The collision is oblique and initially one of theballs was at rest. After the collision, the two balls movewith same speeds. What will be the angle between thevelocities of the balls after the collision?
A plastic ball is dropped from a height of 1 m andrebounds several times from the floor. If 1.03 s elapsefrom the moment it is dropped to the second impactwith the floor, what is the coefficient of restitution?
A shell is fired from a cannon with velocity v m/s at anangleθ with the horizontal direction. At the highest pointin its path it explodes into two pieces of equal mass.One of the pieces retraces its path to the cannon, thenthe speed in m/s of the other piece immediately afterthe explosion is
In perfectly inelastic collisions, the relative velocity ofthe bodies
A ball is let fall from a height h_{0}. There are n collisions with the earth. If the velocity of rebound after n collisions is v_{n} and the ball rises to a height h_{n} , then coefficient of restitution e_{n} is given by
A body X with a momentum p collides with another identical stationary body Y one dimensionally. During the collision, Y gives an impulse J to body X. Then coefficient of restitution is
A particle of mass m moving towards the east with speed v collides with another particle of the same mass and same speed v moving towards the north. If the two particles stick to each other, the new particle of mass 2m will have a speed of
A block of mass 0.50 kg is moving with a speed of 2.00 m/s on a smooth surface. It strikes another stationarymass of 1.00 kg and then they move together as asingle body. The energy loss during the collision is
A pendulum consists of a wooden bob of mass m and of length ι . A bullet of mass m_{1} is fired towards the pendulum with a speed v_{1} . The bullet emerges out of the bob with a speed v_{1}/3 and the bob just completes motion along a vertical circle. Then v_{1} is
Two pendulums each of length ι are initially situated as shown in Fig. The first pendulum is released and strikes the second. Assume that the collision is completely inelastic and neglect the mass of the string and any frictional effects. How high does the centre of mass rise after the collision?
A machinist starts with three identical square platesbut cuts one corner from one of them, two corners fromthe second and three corners from the third. Rank thethree according to the xcoordinate of their centre ofmass, from smallest to largest.
A smooth sphere is moving on a horizontal surfacewith velocity vector 2iˆ + 2 ˆj immediately before it hitsa vertical wall. The wall is parallel toˆj vector and thecoefficient of restitution between the sphere and thewall is e = 1/2. The velocity vector of the sphere after ithits the wall is
Two bodies of masses m and 4m are attached with a string as shown in Fig. The body of mass m hanging from a string of length ι is executing oscillations of angular amplitude 0 θ while the other body is at rest. The minimum coefficient of friction between the mass 4m and the horizontal surface should is
Two equal spheres A and B lie on a smooth horizontal circular groove at opposite ends of a diameter. At time t = 0, A is projected along the groove and it first impinges on B at time t= T_{1} and again at time t= T_{2}. If e is the coefficient of restitution, the ratio T_{2} / T_{1} is
A block ‘A’ of mass w_{1} hits horizontally the rear sideof a spring (ideal) attached to a block B of mass m_{2},resting on a smooth horizontal surface. After hitting,‘A’ gets attached to the spring.
Some statements are given at any moment of time.
i. If velocity of A is greater than B, then kinetic energyof the system will be decreasing.
ii. If velocity of A is greater than B, then kinetic energyof the system will be increasing
iii. If velocity of A is greater then B, them momentumof the system will be decreasing.
iv. If velocity of A is greater than B, then momentumof the system will be increasing.Now select correct alternative :
A particle of mass 4m is projected from the ground atsome angle with horizontal. Its horizontal range is R.At the highest point of its path it breaks into two piecesof masses m and 3m, respectively, such that thesmaller mass comes to rest. The larger mass finallyfalls at a distance x from the point of projection, wherex is equal to
A strip of wood of mass M and length ι is placed on a smooth horizontal surface. An insect of mass m starts at one end of the strip and walks to the other end in time t, moving with a constant speed. The speed of the insect as seen from the ground is
A car of mass m is initially at rest on the boat of mass M tied to the wall of dock through a massless, inextensible string. The car accelerates from rest to velocity v0 in times t0. At t = t0 the car applies brake and comes to rest relative to the boat in negligible time. Neglect friction between the boat and water; the time 't' at which boat will strike the wall is
A train of mass M is moving on a circular track of radius'R' with constant speed V. The length of the train is halfof the perimeter of the track. The linear momentum ofthe train will be
A canon shell moving along a straight line bursts intotwo parts. Just after the burst one part moves withmomentum 20 N s making an angle 30° with the originalline of motion. The minimum momentum of the otherpart of shell just after the burst is
A balloon having mass 'm' is filled with gas and is heldin hands of a boy, Then suddenly it gets released andgas starts coming cout of it with a constant rate. Thevelocity of the ejected gas is also constant (2 m/s) withrespect to the balloon. Find out the velocity of the balloonwhen the mass of gas is reduced to half.
In a vertical plane inside a smooth hollow thin tube, ablock of same mass as that of tube is released as shownin Fig. When it is slightly disturbed it moves towardsright. By the time the block reaches the right end of thetube, the displacement of the tube will be (where 'R' isthe means radius of the tube, assume that the tuberemains in vertical plane)
A stationary body explodes into four identical fragmentssuch that three of them fly off mutually perpendicularto each other, each with same KE, E0. The energy ofexplosion will be
A man stands at one end of the open truck which canrun on frictionless horizontal rails. Initially, the manand the truck are at rest. Man now walks to the otherend and stops. Then which of the following is true?
Figure. shows a thin uniform rod 50 cm long and has amass of 100 g. A hollow metal ball is filled with air andhas a diameter 10 cm and total mass 50 g is fixed toone end of the rod. At what point along its length willthe ball and rod balance horizontally?
A ball is dropped from a height of 45 m from the ground.The coefficient of restitution between the ball and theground is 2/3. What is the distance travelled by theball in 4th second of its motion. Assume negligible timeis spent in rebounding. Let g= 10 ms^{2}.
A bag of mass M hangs by a long massless rope. Abullet of mass m, moving horizontally with velocity u,is caught in the bag. Then for the combined(bag + bullet) system, just after collision
A man stands at one end of a boat which is stationaryin water. Neglect water resistance. The man now movesto the other end of the boat and again becomesstationary. The centre of mass of the ‘man plus boat’system will remain stationary with respect to water
A circular plate of uniform thickness has a diameter of28 cm. A circular portion of diameter 21 cm is removedfrom the plate as shown. O is the centre of mass ofcomplete plate. The position of centre of mass ofremaining portion will shift towards left from ‘O’by
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