Angular Impulse
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365616 Consider a body shown in the figure, consisting of two identical balls, each connected by a light rigid rod. If an impulse \(J=M v(v=\) linear velocity of imparted to the body at one of its ends, what would be its angular velocity?
supporting img

1 \(v / 4 L\)
2 \(2 v / L\)
3 \(v / L\)
4 \(v / 3 L\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365617 A uniform rod \(A B\) of mass \(m\) and length \(l\) at rest on a smooth horizontal surface. An impulse \(P\) is applied to the end \(B\) in a direction which is perpendicular to the length. The time taken by rod to turn through a right angle is :

1 \(2 \pi \dfrac{p}{m l}\)
2 \(2 \pi \dfrac{m l}{p}\)
3 \(\dfrac{\pi p}{m l}\)
4 \(\dfrac{\pi}{12} \dfrac{m l}{p}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365618 An impulse \(J\) is applied on a ring of mass \(m\) along a line passing through its centre \(O\). The ring is placed on a rough horizontal surface. The linear velocity of centre of ring once it starts rolling without slipping is
supporting img

1 \(J/3\;m\)
2 \(J/m\)
3 \(J/4\;m\)
4 \(J/2\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365619 The two uniform discs rotate separately on parallel axles. The upper disc (radius \(a\) and momentum of inertia \(I_{1}\) ) is given an angular velocity \(\omega_{0}\) and the lower disc of (radius \(b\) and momentum of inertia \(I_{2}\) ) is at rest. Now the two discs are moved together so that their rims touch. Final angular velocity of the upper disc is
supporting img

1 \(\dfrac{\left(I_{1} \omega_{0}\right)}{\left[I_{1}+\left(a^{2} I_{2} / b^{2}\right)\right]}\)
2 \(\dfrac{\left(I_{1} \omega_{0}\right)}{\left[I_{1}+\left(b^{2} I_{2} / a^{2}\right)\right]}\)
3 \(\dfrac{\left(I_{2} \omega_{0}\right)}{\left[I_{2}+\left(b^{2} I_{1} / a^{2}\right)\right]}\)
4 \(\dfrac{\left(I_{2} \omega_{0}\right)}{\left[I_{2}+\left(a^{2} I_{1} / b^{2}\right)\right]}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365620 A solid sphere rests on a horizontal surface. A horizontal impulse is applied at a height h above the centre. The sphere starts pure rolling just after the application of impulse. The value of \(\dfrac{h}{r}\) is
supporting img

1 \(\dfrac{1}{2}\)
2 \(\dfrac{2}{3}\)
3 \(\dfrac{1}{5}\)
4 \(\dfrac{2}{5}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365616 Consider a body shown in the figure, consisting of two identical balls, each connected by a light rigid rod. If an impulse \(J=M v(v=\) linear velocity of imparted to the body at one of its ends, what would be its angular velocity?
supporting img

1 \(v / 4 L\)
2 \(2 v / L\)
3 \(v / L\)
4 \(v / 3 L\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365617 A uniform rod \(A B\) of mass \(m\) and length \(l\) at rest on a smooth horizontal surface. An impulse \(P\) is applied to the end \(B\) in a direction which is perpendicular to the length. The time taken by rod to turn through a right angle is :

1 \(2 \pi \dfrac{p}{m l}\)
2 \(2 \pi \dfrac{m l}{p}\)
3 \(\dfrac{\pi p}{m l}\)
4 \(\dfrac{\pi}{12} \dfrac{m l}{p}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365618 An impulse \(J\) is applied on a ring of mass \(m\) along a line passing through its centre \(O\). The ring is placed on a rough horizontal surface. The linear velocity of centre of ring once it starts rolling without slipping is
supporting img

1 \(J/3\;m\)
2 \(J/m\)
3 \(J/4\;m\)
4 \(J/2\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365619 The two uniform discs rotate separately on parallel axles. The upper disc (radius \(a\) and momentum of inertia \(I_{1}\) ) is given an angular velocity \(\omega_{0}\) and the lower disc of (radius \(b\) and momentum of inertia \(I_{2}\) ) is at rest. Now the two discs are moved together so that their rims touch. Final angular velocity of the upper disc is
supporting img

1 \(\dfrac{\left(I_{1} \omega_{0}\right)}{\left[I_{1}+\left(a^{2} I_{2} / b^{2}\right)\right]}\)
2 \(\dfrac{\left(I_{1} \omega_{0}\right)}{\left[I_{1}+\left(b^{2} I_{2} / a^{2}\right)\right]}\)
3 \(\dfrac{\left(I_{2} \omega_{0}\right)}{\left[I_{2}+\left(b^{2} I_{1} / a^{2}\right)\right]}\)
4 \(\dfrac{\left(I_{2} \omega_{0}\right)}{\left[I_{2}+\left(a^{2} I_{1} / b^{2}\right)\right]}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365620 A solid sphere rests on a horizontal surface. A horizontal impulse is applied at a height h above the centre. The sphere starts pure rolling just after the application of impulse. The value of \(\dfrac{h}{r}\) is
supporting img

1 \(\dfrac{1}{2}\)
2 \(\dfrac{2}{3}\)
3 \(\dfrac{1}{5}\)
4 \(\dfrac{2}{5}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365616 Consider a body shown in the figure, consisting of two identical balls, each connected by a light rigid rod. If an impulse \(J=M v(v=\) linear velocity of imparted to the body at one of its ends, what would be its angular velocity?
supporting img

1 \(v / 4 L\)
2 \(2 v / L\)
3 \(v / L\)
4 \(v / 3 L\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365617 A uniform rod \(A B\) of mass \(m\) and length \(l\) at rest on a smooth horizontal surface. An impulse \(P\) is applied to the end \(B\) in a direction which is perpendicular to the length. The time taken by rod to turn through a right angle is :

1 \(2 \pi \dfrac{p}{m l}\)
2 \(2 \pi \dfrac{m l}{p}\)
3 \(\dfrac{\pi p}{m l}\)
4 \(\dfrac{\pi}{12} \dfrac{m l}{p}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365618 An impulse \(J\) is applied on a ring of mass \(m\) along a line passing through its centre \(O\). The ring is placed on a rough horizontal surface. The linear velocity of centre of ring once it starts rolling without slipping is
supporting img

1 \(J/3\;m\)
2 \(J/m\)
3 \(J/4\;m\)
4 \(J/2\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365619 The two uniform discs rotate separately on parallel axles. The upper disc (radius \(a\) and momentum of inertia \(I_{1}\) ) is given an angular velocity \(\omega_{0}\) and the lower disc of (radius \(b\) and momentum of inertia \(I_{2}\) ) is at rest. Now the two discs are moved together so that their rims touch. Final angular velocity of the upper disc is
supporting img

1 \(\dfrac{\left(I_{1} \omega_{0}\right)}{\left[I_{1}+\left(a^{2} I_{2} / b^{2}\right)\right]}\)
2 \(\dfrac{\left(I_{1} \omega_{0}\right)}{\left[I_{1}+\left(b^{2} I_{2} / a^{2}\right)\right]}\)
3 \(\dfrac{\left(I_{2} \omega_{0}\right)}{\left[I_{2}+\left(b^{2} I_{1} / a^{2}\right)\right]}\)
4 \(\dfrac{\left(I_{2} \omega_{0}\right)}{\left[I_{2}+\left(a^{2} I_{1} / b^{2}\right)\right]}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365620 A solid sphere rests on a horizontal surface. A horizontal impulse is applied at a height h above the centre. The sphere starts pure rolling just after the application of impulse. The value of \(\dfrac{h}{r}\) is
supporting img

1 \(\dfrac{1}{2}\)
2 \(\dfrac{2}{3}\)
3 \(\dfrac{1}{5}\)
4 \(\dfrac{2}{5}\)
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365616 Consider a body shown in the figure, consisting of two identical balls, each connected by a light rigid rod. If an impulse \(J=M v(v=\) linear velocity of imparted to the body at one of its ends, what would be its angular velocity?
supporting img

1 \(v / 4 L\)
2 \(2 v / L\)
3 \(v / L\)
4 \(v / 3 L\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365617 A uniform rod \(A B\) of mass \(m\) and length \(l\) at rest on a smooth horizontal surface. An impulse \(P\) is applied to the end \(B\) in a direction which is perpendicular to the length. The time taken by rod to turn through a right angle is :

1 \(2 \pi \dfrac{p}{m l}\)
2 \(2 \pi \dfrac{m l}{p}\)
3 \(\dfrac{\pi p}{m l}\)
4 \(\dfrac{\pi}{12} \dfrac{m l}{p}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365618 An impulse \(J\) is applied on a ring of mass \(m\) along a line passing through its centre \(O\). The ring is placed on a rough horizontal surface. The linear velocity of centre of ring once it starts rolling without slipping is
supporting img

1 \(J/3\;m\)
2 \(J/m\)
3 \(J/4\;m\)
4 \(J/2\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365619 The two uniform discs rotate separately on parallel axles. The upper disc (radius \(a\) and momentum of inertia \(I_{1}\) ) is given an angular velocity \(\omega_{0}\) and the lower disc of (radius \(b\) and momentum of inertia \(I_{2}\) ) is at rest. Now the two discs are moved together so that their rims touch. Final angular velocity of the upper disc is
supporting img

1 \(\dfrac{\left(I_{1} \omega_{0}\right)}{\left[I_{1}+\left(a^{2} I_{2} / b^{2}\right)\right]}\)
2 \(\dfrac{\left(I_{1} \omega_{0}\right)}{\left[I_{1}+\left(b^{2} I_{2} / a^{2}\right)\right]}\)
3 \(\dfrac{\left(I_{2} \omega_{0}\right)}{\left[I_{2}+\left(b^{2} I_{1} / a^{2}\right)\right]}\)
4 \(\dfrac{\left(I_{2} \omega_{0}\right)}{\left[I_{2}+\left(a^{2} I_{1} / b^{2}\right)\right]}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365620 A solid sphere rests on a horizontal surface. A horizontal impulse is applied at a height h above the centre. The sphere starts pure rolling just after the application of impulse. The value of \(\dfrac{h}{r}\) is
supporting img

1 \(\dfrac{1}{2}\)
2 \(\dfrac{2}{3}\)
3 \(\dfrac{1}{5}\)
4 \(\dfrac{2}{5}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365616 Consider a body shown in the figure, consisting of two identical balls, each connected by a light rigid rod. If an impulse \(J=M v(v=\) linear velocity of imparted to the body at one of its ends, what would be its angular velocity?
supporting img

1 \(v / 4 L\)
2 \(2 v / L\)
3 \(v / L\)
4 \(v / 3 L\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365617 A uniform rod \(A B\) of mass \(m\) and length \(l\) at rest on a smooth horizontal surface. An impulse \(P\) is applied to the end \(B\) in a direction which is perpendicular to the length. The time taken by rod to turn through a right angle is :

1 \(2 \pi \dfrac{p}{m l}\)
2 \(2 \pi \dfrac{m l}{p}\)
3 \(\dfrac{\pi p}{m l}\)
4 \(\dfrac{\pi}{12} \dfrac{m l}{p}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365618 An impulse \(J\) is applied on a ring of mass \(m\) along a line passing through its centre \(O\). The ring is placed on a rough horizontal surface. The linear velocity of centre of ring once it starts rolling without slipping is
supporting img

1 \(J/3\;m\)
2 \(J/m\)
3 \(J/4\;m\)
4 \(J/2\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365619 The two uniform discs rotate separately on parallel axles. The upper disc (radius \(a\) and momentum of inertia \(I_{1}\) ) is given an angular velocity \(\omega_{0}\) and the lower disc of (radius \(b\) and momentum of inertia \(I_{2}\) ) is at rest. Now the two discs are moved together so that their rims touch. Final angular velocity of the upper disc is
supporting img

1 \(\dfrac{\left(I_{1} \omega_{0}\right)}{\left[I_{1}+\left(a^{2} I_{2} / b^{2}\right)\right]}\)
2 \(\dfrac{\left(I_{1} \omega_{0}\right)}{\left[I_{1}+\left(b^{2} I_{2} / a^{2}\right)\right]}\)
3 \(\dfrac{\left(I_{2} \omega_{0}\right)}{\left[I_{2}+\left(b^{2} I_{1} / a^{2}\right)\right]}\)
4 \(\dfrac{\left(I_{2} \omega_{0}\right)}{\left[I_{2}+\left(a^{2} I_{1} / b^{2}\right)\right]}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365620 A solid sphere rests on a horizontal surface. A horizontal impulse is applied at a height h above the centre. The sphere starts pure rolling just after the application of impulse. The value of \(\dfrac{h}{r}\) is
supporting img

1 \(\dfrac{1}{2}\)
2 \(\dfrac{2}{3}\)
3 \(\dfrac{1}{5}\)
4 \(\dfrac{2}{5}\)