EASY
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IMPORTANT
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Statement-1: In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.

Statement-2: In an elastic collision, the linear momentum of the system is conserved.

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Important Questions on Centre of Mass, Momentum and Collisions

EASY
JEE Main/Advance
IMPORTANT
Two balls having linear momenta p1=pi^ and p2=-pi^, undergo a collision in free space. There is no external force acting on the balls. Let p1' and p2' be their final momenta. The following option (s) is (are) not allowed for any non-zero value of p, a1, a2, b1, b2, c1 and c2.
EASY
JEE Main/Advance
IMPORTANT

Look at the drawing given in the figure which has been drawn with ink of uniform line-thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments is m. The mass of the ink used to draw the outer circle is 6m. The coordinates of the centres of the different part are: outer circle (0, 0), left inner circle (a, a), right inner circle (a, a), vertical line (0, 0) and horizontal line (0, a). The y-coordinate of the centre of mass of the ink in this drawing is

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MEDIUM
JEE Main/Advance
IMPORTANT

Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are v and 2v, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at A, these two particles will again reach the point A?

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HARD
JEE Main/Advance
IMPORTANT
A point mass of 1 kg collides elastically with a stationary mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 m s-1. Which of the following statement(s) is (are) correct for the system of these two masses
EASY
JEE Main/Advance
IMPORTANT

A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, travelling with a velocity V ms-1 in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The initial velocity V of the bullet is

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MEDIUM
JEE Main/Advance
IMPORTANT
A particle of mass m is projected from the ground with the initial speed u0 at an angle α with the horizontal. At the highest point of the trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u0. The angle that the composite system makes with horizontal immediately after the collision is
MEDIUM
JEE Main/Advance
IMPORTANT

A block of mass M has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at x = 0, in a coordinate system fixed to the table. A point mass m is released from rest at the topmost point of the path as shown and its slides down. When the mass loses contact with the block, its position is x and the velocity is v. At the instant, which of the following options is/are correct ?

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HARD
JEE Main/Advance
IMPORTANT

A circular disc of radius R  is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is  αR  from the centre of the bigger disc. The value of α is.