Two balls A and B of masses \(0.3kg\) and \(0.2kg\) respectively are moving in a straight line. Ball A moving along (+)X-axis with a velocity \(2\frac{m}{s}\) and ball B is moving along (-)X-Axis with a velocity \(2\frac{m}{s}\) approaches each-other. The head on collision occurs between the balls and then they move along the direction opposite to each others original direction. Calculate: (i) Velocity of ball A and ball B after the collision? (ii) Total K.E of balls before and after the collision?
Ans:(i) \(\vec{V_{1}}=1.2(-\hat{i})\frac{m}{s}\) & \(\vec{V_{2}}=2.8(+\hat{i})\frac{m}{s}\) and (ii) \(E=0.216+0.784=1J\)
Two ball bearings of mass \(m\) each moving in opposite direction with equal speeds \(v\), collide head on with each other.Predict the outcome of the collision, assuming it to be perfectly elastic.
Ans: \(V_{1}=v\) and \(V_{2}= v\).
A body of mass \(3kg\) makes an elastic collision with another body at rest and continues to move in the original direction with the speed equal to the \(\frac{1}{3}\) of its original speed, Find: the mass of the second body.
Ans: \(m_{2}=1.5kg\).
A body of mass \(M\) is at rest is struck by a moving body of mass \(m\). Prove; that the fraction of the initial kinetic energy of the mass \(m\) transferred to the struck body is \(\frac{4mM}{(m+M)^{2}}\) in an elastic collision.
A ball is dropped from a height of \(h\). It rebounds from ground a number of times. If the coefficient of restitution is \(e\), to what height does it go after \(n^{TH}\) rebounding?
Ans: \(H=he^{2n}\).
A sphere is having a mass \(m\) moving with a velocity \(u\) hits another stationary sphere of same mass. If, \(e\) be the co-efficient of restitution, what is the ration of the velocities of sphere after collision?
Ans: \(\frac{V_{1}}{V_{2}}=\frac{1+e}{1-e}\).
Two balls falls under gravity from a height of \(10m\) with an initial downward velocity \(u\). It collide with the ground, losses \(50\%\) of its energy in collision and then rises back to the same height . Find: The initial velocity \(u\).
Ans: \(u=14\frac{m}{s}\).
A ball moving with a speed of \(9\frac{m}{s}\) strikes an identical ball such that after collision the direction of movement of each ball makes an angle of \(30^{o}\) with the original line of motion. Find: the speeds of two balls after the collision. Is the kinetic energy is conserved in the collision?
Ans: \(V_{1}=V_{2}=3\sqrt{3}\frac{m}{s}\). and K.E is not conserved.
Two billiard ball of masses \(m_{1}\) and \(m_{2}\). The first ball is called as the cue and the second ball is called as target. The billiard player wants to sink the target ball in the corner pocket, Which is at an angle of \(\phi\) and if cue ball deflects by \(\theta=37^{o}\) from its initial path. Assume that the collision is elastic and that friction & rotational motion are not import . Find: \(\phi\)?.
Ans: \(\phi=53^{o}\).
A ball is moving with velocity \(2\frac{m}{s}\) collides head on with another stationary ball of double the mass. If, the coefficient of restitution is \(0.5\). Find: their velocities after the collision.
Ans: \(V_{1}=0(Zero)\) and \(V_{2}=1\frac{m}{s}\).
A mass \(m\) moves with a velocity \(v\) and collides in-elastically with another identical mass. After collision, the first mass moves with velocity \(\frac{v}{\sqrt{3}}\) in a direction perpendicular to the initial direction of the motion. Find: the speed of second mass after collision.
Ans: \(v’=\frac{2v}{\sqrt{3}}\).
A ball is dropped from a height of \(3.6m\). It rebounds from horizontal surface to a height of \(1.6m\). Find; the co-efficient of restitution?
Ans: \(e=0.667\).
A ball is dropped freely from a height \(“h”\). The ball is continuously rebounding then find out: (i) Velocity of the ball after \(n^{th}\) rebounds? (ii) Height attained by the ball after \(“n^{th}”\) rebounds? (iii) Time taken by ball in \(n^{th}\) rebound? (iv) Total distance covered by the ball before it stops rebounding?
A ball is dropped from a height of \(h\) on to a floor. If the co-efficient of the restitution is \(e\). calculate: the height up to which the ball first rebounds?
Ans: \(e^{2}h\).
A body of mass \(M\) at rest is struck by a body of mass \(m\). Shows that the fraction of \(K.E\) of the mass \(m\) transffered to the struck particle is \(\frac{4mM}{\left(m+M\right)^{2}}\).
