149957 A cyclist rides up a hill with constant velocity. When he exerts an average force of \(20 \mathrm{~kg}\)-wt on the \(50 \mathrm{~cm}\) pedal rod. It completes 6 revolutions in \(4 \mathrm{~s}\). The power developed by cyclist is

149958 A billiard ball of diameter \(5 \mathrm{~cm}\) at rest is hit by a cue at a height \(0.5 \mathrm{~cm}\) above its centre. If it rolls with a linear velocity of \(10 \mathrm{~ms}^{-1}\), then its angular velocity is

149959 A uniform rod \(A B\) of mass ' \(m\) ' and length ' \(2 l\) ' is falling freely without rotation under gravity with \(A B\) horizontal. Suddenly the end \(A\) is fixed when the speed of the rod is ' \(v\) '. The angular speed with which the rod begins to rotate is

149960 A rigid uniform rod of mass ' \(M\) ' and length ' \(L\) ' is resting on a smooth horizontal table. It is pivoted at its centre. Two marbles each of mass \(\frac{M}{6}\) moving with uniform speed \(L \mathrm{~ms}^{-1}\) in the plane of the table collide with the two ends of the rod simultaneously as shown in the figure. The marbles stuck to the rod and continue to move with the rod. Time taken by the rod to rotate through an angle \(\frac{\pi}{2}\) radian is (in seconds)

149957 A cyclist rides up a hill with constant velocity. When he exerts an average force of \(20 \mathrm{~kg}\)-wt on the \(50 \mathrm{~cm}\) pedal rod. It completes 6 revolutions in \(4 \mathrm{~s}\). The power developed by cyclist is

149958 A billiard ball of diameter \(5 \mathrm{~cm}\) at rest is hit by a cue at a height \(0.5 \mathrm{~cm}\) above its centre. If it rolls with a linear velocity of \(10 \mathrm{~ms}^{-1}\), then its angular velocity is

149959 A uniform rod \(A B\) of mass ' \(m\) ' and length ' \(2 l\) ' is falling freely without rotation under gravity with \(A B\) horizontal. Suddenly the end \(A\) is fixed when the speed of the rod is ' \(v\) '. The angular speed with which the rod begins to rotate is

149960 A rigid uniform rod of mass ' \(M\) ' and length ' \(L\) ' is resting on a smooth horizontal table. It is pivoted at its centre. Two marbles each of mass \(\frac{M}{6}\) moving with uniform speed \(L \mathrm{~ms}^{-1}\) in the plane of the table collide with the two ends of the rod simultaneously as shown in the figure. The marbles stuck to the rod and continue to move with the rod. Time taken by the rod to rotate through an angle \(\frac{\pi}{2}\) radian is (in seconds)

149957 A cyclist rides up a hill with constant velocity. When he exerts an average force of \(20 \mathrm{~kg}\)-wt on the \(50 \mathrm{~cm}\) pedal rod. It completes 6 revolutions in \(4 \mathrm{~s}\). The power developed by cyclist is

149958 A billiard ball of diameter \(5 \mathrm{~cm}\) at rest is hit by a cue at a height \(0.5 \mathrm{~cm}\) above its centre. If it rolls with a linear velocity of \(10 \mathrm{~ms}^{-1}\), then its angular velocity is

149959 A uniform rod \(A B\) of mass ' \(m\) ' and length ' \(2 l\) ' is falling freely without rotation under gravity with \(A B\) horizontal. Suddenly the end \(A\) is fixed when the speed of the rod is ' \(v\) '. The angular speed with which the rod begins to rotate is

149960 A rigid uniform rod of mass ' \(M\) ' and length ' \(L\) ' is resting on a smooth horizontal table. It is pivoted at its centre. Two marbles each of mass \(\frac{M}{6}\) moving with uniform speed \(L \mathrm{~ms}^{-1}\) in the plane of the table collide with the two ends of the rod simultaneously as shown in the figure. The marbles stuck to the rod and continue to move with the rod. Time taken by the rod to rotate through an angle \(\frac{\pi}{2}\) radian is (in seconds)

149957 A cyclist rides up a hill with constant velocity. When he exerts an average force of \(20 \mathrm{~kg}\)-wt on the \(50 \mathrm{~cm}\) pedal rod. It completes 6 revolutions in \(4 \mathrm{~s}\). The power developed by cyclist is

149958 A billiard ball of diameter \(5 \mathrm{~cm}\) at rest is hit by a cue at a height \(0.5 \mathrm{~cm}\) above its centre. If it rolls with a linear velocity of \(10 \mathrm{~ms}^{-1}\), then its angular velocity is

149959 A uniform rod \(A B\) of mass ' \(m\) ' and length ' \(2 l\) ' is falling freely without rotation under gravity with \(A B\) horizontal. Suddenly the end \(A\) is fixed when the speed of the rod is ' \(v\) '. The angular speed with which the rod begins to rotate is

149960 A rigid uniform rod of mass ' \(M\) ' and length ' \(L\) ' is resting on a smooth horizontal table. It is pivoted at its centre. Two marbles each of mass \(\frac{M}{6}\) moving with uniform speed \(L \mathrm{~ms}^{-1}\) in the plane of the table collide with the two ends of the rod simultaneously as shown in the figure. The marbles stuck to the rod and continue to move with the rod. Time taken by the rod to rotate through an angle \(\frac{\pi}{2}\) radian is (in seconds)