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Rotational Motion

269597 Four identical planks each of lengths ' \(L\) ' are arranged one above the other over a table as shown. Each projects a distance 'a' beyond the edge of the one that is below it. What is the maximum possible value of ' \(a\) ' for the system to be in equilibrium without tripping forward?

1 \(\mathrm{L} / 5\)

2 \(\mathrm{L} / 4\)

3 \(\mathrm{L} / 3\)

4 \(\mathrm{L}\)

Rotational Motion

269598 Two masses ' \(m_{1}\) ' and ' \(m_{2}\) ' \(\left(m_{1}\lt m_{2}\right)\) are connected to the ends of a light inextensible string which passes over the surface of a smooth fixed pulley. If the system is released from rest, the acceleration of the centre of mass of the system will be ( \(g=\) acceleration due to gravity)

1 \(\frac{g\left(m_{1}-m_{2}\right)}{\left(m_{1}+m_{2}\right)}\)

2 \(\frac{g\left(m_{1}-m_{2}\right)^{2}}{\left(m_{1}+m_{2}\right)^{2}}\)

3 \(\frac{g\left(\mathrm{~m}_{1}+\mathrm{m}_{2}\right)}{\left(m_{1}-m_{2}\right)}\)

4 \(\frac{g\left(\mathrm{~m}_{1}+\mathrm{m}_{2}\right)}{\left(m_{1}-m_{2}\right)}\)

Rotational Motion

269599 Two bodies of masses \(m_{1}\) and \(m_{2}\) are moving with velocity \(v_{1}\) and \(v_{2}\) respectively in the same direction. The total momentum of the system in the frame of reference attached to the centre of mass is ( \(v\) is relative velocity between the masses)

1 \(\frac{m_{1} m_{2} v}{m_{1}-m_{2}}\)

2 \(\frac{2 \mathrm{~m}_{1} \mathrm{~m}_{2} \mathrm{v}}{m_{1}+m_{2}}\)

3 zero

4 \(\frac{4 \mathrm{~m}_{1} \mathrm{~m}_{2} \mathrm{v}}{m_{1}+m_{2}}\)

Rotational Motion

269600 A shell in flight explodes into \(n\) equal fragments \(k\) of the fragments reach the ground earlier than the other fragments. The acceleration of their centre of mass subsequently will be

1 \(g\)

2 \(n-k) g\)

3 \(\frac{(n-k) g}{k}\)

4 \(\frac{(n-k)}{n} g\)

Rotational Motion

269597 Four identical planks each of lengths ' \(L\) ' are arranged one above the other over a table as shown. Each projects a distance 'a' beyond the edge of the one that is below it. What is the maximum possible value of ' \(a\) ' for the system to be in equilibrium without tripping forward?

1 \(\mathrm{L} / 5\)

2 \(\mathrm{L} / 4\)

3 \(\mathrm{L} / 3\)

4 \(\mathrm{L}\)

Rotational Motion

269598 Two masses ' \(m_{1}\) ' and ' \(m_{2}\) ' \(\left(m_{1}\lt m_{2}\right)\) are connected to the ends of a light inextensible string which passes over the surface of a smooth fixed pulley. If the system is released from rest, the acceleration of the centre of mass of the system will be ( \(g=\) acceleration due to gravity)

1 \(\frac{g\left(m_{1}-m_{2}\right)}{\left(m_{1}+m_{2}\right)}\)

2 \(\frac{g\left(m_{1}-m_{2}\right)^{2}}{\left(m_{1}+m_{2}\right)^{2}}\)

3 \(\frac{g\left(\mathrm{~m}_{1}+\mathrm{m}_{2}\right)}{\left(m_{1}-m_{2}\right)}\)

4 \(\frac{g\left(\mathrm{~m}_{1}+\mathrm{m}_{2}\right)}{\left(m_{1}-m_{2}\right)}\)

Rotational Motion

269599 Two bodies of masses \(m_{1}\) and \(m_{2}\) are moving with velocity \(v_{1}\) and \(v_{2}\) respectively in the same direction. The total momentum of the system in the frame of reference attached to the centre of mass is ( \(v\) is relative velocity between the masses)

1 \(\frac{m_{1} m_{2} v}{m_{1}-m_{2}}\)

2 \(\frac{2 \mathrm{~m}_{1} \mathrm{~m}_{2} \mathrm{v}}{m_{1}+m_{2}}\)

3 zero

4 \(\frac{4 \mathrm{~m}_{1} \mathrm{~m}_{2} \mathrm{v}}{m_{1}+m_{2}}\)

Rotational Motion

269600 A shell in flight explodes into \(n\) equal fragments \(k\) of the fragments reach the ground earlier than the other fragments. The acceleration of their centre of mass subsequently will be

1 \(g\)

2 \(n-k) g\)

3 \(\frac{(n-k) g}{k}\)

4 \(\frac{(n-k)}{n} g\)

Rotational Motion

269597 Four identical planks each of lengths ' \(L\) ' are arranged one above the other over a table as shown. Each projects a distance 'a' beyond the edge of the one that is below it. What is the maximum possible value of ' \(a\) ' for the system to be in equilibrium without tripping forward?

1 \(\mathrm{L} / 5\)

2 \(\mathrm{L} / 4\)

3 \(\mathrm{L} / 3\)

4 \(\mathrm{L}\)

Rotational Motion

269598 Two masses ' \(m_{1}\) ' and ' \(m_{2}\) ' \(\left(m_{1}\lt m_{2}\right)\) are connected to the ends of a light inextensible string which passes over the surface of a smooth fixed pulley. If the system is released from rest, the acceleration of the centre of mass of the system will be ( \(g=\) acceleration due to gravity)

1 \(\frac{g\left(m_{1}-m_{2}\right)}{\left(m_{1}+m_{2}\right)}\)

2 \(\frac{g\left(m_{1}-m_{2}\right)^{2}}{\left(m_{1}+m_{2}\right)^{2}}\)

3 \(\frac{g\left(\mathrm{~m}_{1}+\mathrm{m}_{2}\right)}{\left(m_{1}-m_{2}\right)}\)

4 \(\frac{g\left(\mathrm{~m}_{1}+\mathrm{m}_{2}\right)}{\left(m_{1}-m_{2}\right)}\)

Rotational Motion

269599 Two bodies of masses \(m_{1}\) and \(m_{2}\) are moving with velocity \(v_{1}\) and \(v_{2}\) respectively in the same direction. The total momentum of the system in the frame of reference attached to the centre of mass is ( \(v\) is relative velocity between the masses)

1 \(\frac{m_{1} m_{2} v}{m_{1}-m_{2}}\)

2 \(\frac{2 \mathrm{~m}_{1} \mathrm{~m}_{2} \mathrm{v}}{m_{1}+m_{2}}\)

3 zero

4 \(\frac{4 \mathrm{~m}_{1} \mathrm{~m}_{2} \mathrm{v}}{m_{1}+m_{2}}\)

Rotational Motion

269600 A shell in flight explodes into \(n\) equal fragments \(k\) of the fragments reach the ground earlier than the other fragments. The acceleration of their centre of mass subsequently will be

1 \(g\)

2 \(n-k) g\)

3 \(\frac{(n-k) g}{k}\)

4 \(\frac{(n-k)}{n} g\)

Rotational Motion

269597 Four identical planks each of lengths ' \(L\) ' are arranged one above the other over a table as shown. Each projects a distance 'a' beyond the edge of the one that is below it. What is the maximum possible value of ' \(a\) ' for the system to be in equilibrium without tripping forward?

1 \(\mathrm{L} / 5\)

2 \(\mathrm{L} / 4\)

3 \(\mathrm{L} / 3\)

4 \(\mathrm{L}\)

Rotational Motion

269598 Two masses ' \(m_{1}\) ' and ' \(m_{2}\) ' \(\left(m_{1}\lt m_{2}\right)\) are connected to the ends of a light inextensible string which passes over the surface of a smooth fixed pulley. If the system is released from rest, the acceleration of the centre of mass of the system will be ( \(g=\) acceleration due to gravity)

1 \(\frac{g\left(m_{1}-m_{2}\right)}{\left(m_{1}+m_{2}\right)}\)

2 \(\frac{g\left(m_{1}-m_{2}\right)^{2}}{\left(m_{1}+m_{2}\right)^{2}}\)

3 \(\frac{g\left(\mathrm{~m}_{1}+\mathrm{m}_{2}\right)}{\left(m_{1}-m_{2}\right)}\)

4 \(\frac{g\left(\mathrm{~m}_{1}+\mathrm{m}_{2}\right)}{\left(m_{1}-m_{2}\right)}\)

Rotational Motion

269599 Two bodies of masses \(m_{1}\) and \(m_{2}\) are moving with velocity \(v_{1}\) and \(v_{2}\) respectively in the same direction. The total momentum of the system in the frame of reference attached to the centre of mass is ( \(v\) is relative velocity between the masses)

1 \(\frac{m_{1} m_{2} v}{m_{1}-m_{2}}\)

2 \(\frac{2 \mathrm{~m}_{1} \mathrm{~m}_{2} \mathrm{v}}{m_{1}+m_{2}}\)

3 zero

4 \(\frac{4 \mathrm{~m}_{1} \mathrm{~m}_{2} \mathrm{v}}{m_{1}+m_{2}}\)

Rotational Motion

269600 A shell in flight explodes into \(n\) equal fragments \(k\) of the fragments reach the ground earlier than the other fragments. The acceleration of their centre of mass subsequently will be

1 \(g\)

2 \(n-k) g\)

3 \(\frac{(n-k) g}{k}\)

4 \(\frac{(n-k)}{n} g\)

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