As per the given figure, a small ball \(P\) slides down the quadrant of a circle and hits the other ball \(Q\) of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball \(Q\) after collision will be \(............\,m/s\) \(:\left( g =10\,m / s ^2\right)\)

In a system two particles of masses \(m_1=3 \mathrm{~kg}\) and \(\mathrm{m}_2=2 \mathrm{~kg}\) are placed at certain distance from each other. The particle of mass \(m_1\) is moved towards the center of mass of the system through a distance \(2 \mathrm{~cm}\). In order to keep the center of mass of the system at the original position, the particle of mass \(\mathrm{m}_2\) should move towards the center of mass by the distance _______\(\mathrm{cm}\).

Consider a cylinder of mass \(M\) resting on a rough horizontal rug that is pulled out from under it with acceleration \('a'\) perpendicular to the axis of the cylinder. What is \(F_{friction}\) at point \(P\) ? It is assumed that the cylinder does not slip

A tennis ball (treated as hollow spherical shell) starting from \(O\) rolls down a hill. At point \(A\) the ball becomes air borne leaving at an angle of \(30^o\) with the horizontal. The ball strikes the ground at \(B\). What is the value of the distance \(AB\) ? (Moment of inertia of a spherical shell of mass \(m\) and radius \(R\) about its diameter .......... \(m\). \(= \frac {2}{3}\,mR^2\))

\(A\) and \(B\) are two sources generating sound waves. A listener is situated at \(C\) . The frequency of the source at \(A\) is \(500\,Hz\) . \(A,\) now, moves towards \(C\) with a speed \(4\,m/s.\) The number of beats heard at \(C\) is \(6.\) When \(A\) moves away from \(C\) with speed \(4\,m/s,\) the number of beats heard at \(C\) is \(18.\) The speed of sound is \(340\,m/s.\) The frequency of the source at \(B\) is ..... \(Hz\)

The activity of a radioactive sample falls from \(700 \;\mathrm{s}^{-1}\) to \(500\; \mathrm{s}^{-1}\) in \(30\;min\). Its half life is close to.........\(min\)

A car is moving with a constant speed of \(20\,m / s\) in a circular horizontal track of radius \(40\,m\). A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take \(g =10\) \(\left.m / s ^2\right)\)

Two wires A and B are made of same material having ratio of lengths \(\frac{L_A}{L_B}=\frac{1}{3}\) and their diameters ratio \(\frac{d_A}{d_B}=2\). If both the wires are stretched using same force, what would be the ratio of their respective elongations?

As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of \(45^{\circ}\) with the load axis. The length of wire is \(62.8\,cm\) and its diameter is \(4\,mm\). The Young's modulus is found to be \(x \times\) \(10^4\,Nm ^{-2}\). The value of \(x\) is

Given below are two statements: Statement \(I :\) In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution. Statement \(II :\) In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule. In the light of the above statements, choose the correct answer from the options given below:

A bead of mass \(m\) stays at point \(P ( a , b )\) on a wire bent in the shape of a parabola \(y=4 Cx ^{2}\) and rotating with angular speed \(\omega\) (see figure). The value of \(\omega\) is (neglect friction)