00. Centre of Mass
Rotational Motion

149749 Two particles of masses \(m_{1}\) and \(m_{2}\left(m_{1}>m_{2}\right)\), initially at rest, move towards each other under an inverse square law force of attraction. Pick out the correct statement about the centre of mass (CM) of the system

1 The CM moves towards \(m_{1}\).
2 The CM moves towards \(\mathrm{m}_{2}\).
3 The CM remains at rest.
4 The motion of CM is accelerated.
Rotational Motion

149755 A car of mass \(M\) is tied to one end of a massless rope of length \(10 \mathrm{~m}\). The other end of the rope is in the hands of a man of mass \(M\). The entire system is on a smooth horizontal surface. The man is at \(x=0\) and the cart at \(x=10 \mathrm{~m}\). If the man pulls the cart by the rope, the man and the cart will meet at the point

1 they will never meet
2 \(x=10 \mathrm{~m}\)
3 \(x=5 \mathrm{~m}\)
4 \(x=0\)
Rotational Motion

149756 Three identical metal balls each of radius \(r\) are placed touching each other on a horizontal surface such that an equilateral triangle is formed with centers of three balls joined. The centre of mass of the system is located at

1 horizontal surface
2 centre of one of the balls
3 line joining the centers of any two balls
4 point of intersection of the medians
Rotational Motion

149758 A solid sphere of radius \(R\) is placed on a smooth horizontal surface. A horizontal force \(F\) is applied at height \(h\) from the lowest point. For the maximum acceleration of the centre of mass

1 \(h=R\)
2 \(\mathrm{h}=2 \mathrm{R}\)
3 \(\mathrm{h}=0\)
4 the acceleration will be same and there is no relation between \(h\) and \(R\)
Rotational Motion

269276 When a force is applied on a body, Newton's second law is applicable to

1 center of mass
2 any part of the body
3 upper most part of body
4 lower most part of body
Rotational Motion

149749 Two particles of masses \(m_{1}\) and \(m_{2}\left(m_{1}>m_{2}\right)\), initially at rest, move towards each other under an inverse square law force of attraction. Pick out the correct statement about the centre of mass (CM) of the system

1 The CM moves towards \(m_{1}\).
2 The CM moves towards \(\mathrm{m}_{2}\).
3 The CM remains at rest.
4 The motion of CM is accelerated.
Rotational Motion

149755 A car of mass \(M\) is tied to one end of a massless rope of length \(10 \mathrm{~m}\). The other end of the rope is in the hands of a man of mass \(M\). The entire system is on a smooth horizontal surface. The man is at \(x=0\) and the cart at \(x=10 \mathrm{~m}\). If the man pulls the cart by the rope, the man and the cart will meet at the point

1 they will never meet
2 \(x=10 \mathrm{~m}\)
3 \(x=5 \mathrm{~m}\)
4 \(x=0\)
Rotational Motion

149756 Three identical metal balls each of radius \(r\) are placed touching each other on a horizontal surface such that an equilateral triangle is formed with centers of three balls joined. The centre of mass of the system is located at

1 horizontal surface
2 centre of one of the balls
3 line joining the centers of any two balls
4 point of intersection of the medians
Rotational Motion

149758 A solid sphere of radius \(R\) is placed on a smooth horizontal surface. A horizontal force \(F\) is applied at height \(h\) from the lowest point. For the maximum acceleration of the centre of mass

1 \(h=R\)
2 \(\mathrm{h}=2 \mathrm{R}\)
3 \(\mathrm{h}=0\)
4 the acceleration will be same and there is no relation between \(h\) and \(R\)
Rotational Motion

269276 When a force is applied on a body, Newton's second law is applicable to

1 center of mass
2 any part of the body
3 upper most part of body
4 lower most part of body
Rotational Motion

149749 Two particles of masses \(m_{1}\) and \(m_{2}\left(m_{1}>m_{2}\right)\), initially at rest, move towards each other under an inverse square law force of attraction. Pick out the correct statement about the centre of mass (CM) of the system

1 The CM moves towards \(m_{1}\).
2 The CM moves towards \(\mathrm{m}_{2}\).
3 The CM remains at rest.
4 The motion of CM is accelerated.
Rotational Motion

149755 A car of mass \(M\) is tied to one end of a massless rope of length \(10 \mathrm{~m}\). The other end of the rope is in the hands of a man of mass \(M\). The entire system is on a smooth horizontal surface. The man is at \(x=0\) and the cart at \(x=10 \mathrm{~m}\). If the man pulls the cart by the rope, the man and the cart will meet at the point

1 they will never meet
2 \(x=10 \mathrm{~m}\)
3 \(x=5 \mathrm{~m}\)
4 \(x=0\)
Rotational Motion

149756 Three identical metal balls each of radius \(r\) are placed touching each other on a horizontal surface such that an equilateral triangle is formed with centers of three balls joined. The centre of mass of the system is located at

1 horizontal surface
2 centre of one of the balls
3 line joining the centers of any two balls
4 point of intersection of the medians
Rotational Motion

149758 A solid sphere of radius \(R\) is placed on a smooth horizontal surface. A horizontal force \(F\) is applied at height \(h\) from the lowest point. For the maximum acceleration of the centre of mass

1 \(h=R\)
2 \(\mathrm{h}=2 \mathrm{R}\)
3 \(\mathrm{h}=0\)
4 the acceleration will be same and there is no relation between \(h\) and \(R\)
Rotational Motion

269276 When a force is applied on a body, Newton's second law is applicable to

1 center of mass
2 any part of the body
3 upper most part of body
4 lower most part of body
Rotational Motion

149749 Two particles of masses \(m_{1}\) and \(m_{2}\left(m_{1}>m_{2}\right)\), initially at rest, move towards each other under an inverse square law force of attraction. Pick out the correct statement about the centre of mass (CM) of the system

1 The CM moves towards \(m_{1}\).
2 The CM moves towards \(\mathrm{m}_{2}\).
3 The CM remains at rest.
4 The motion of CM is accelerated.
Rotational Motion

149755 A car of mass \(M\) is tied to one end of a massless rope of length \(10 \mathrm{~m}\). The other end of the rope is in the hands of a man of mass \(M\). The entire system is on a smooth horizontal surface. The man is at \(x=0\) and the cart at \(x=10 \mathrm{~m}\). If the man pulls the cart by the rope, the man and the cart will meet at the point

1 they will never meet
2 \(x=10 \mathrm{~m}\)
3 \(x=5 \mathrm{~m}\)
4 \(x=0\)
Rotational Motion

149756 Three identical metal balls each of radius \(r\) are placed touching each other on a horizontal surface such that an equilateral triangle is formed with centers of three balls joined. The centre of mass of the system is located at

1 horizontal surface
2 centre of one of the balls
3 line joining the centers of any two balls
4 point of intersection of the medians
Rotational Motion

149758 A solid sphere of radius \(R\) is placed on a smooth horizontal surface. A horizontal force \(F\) is applied at height \(h\) from the lowest point. For the maximum acceleration of the centre of mass

1 \(h=R\)
2 \(\mathrm{h}=2 \mathrm{R}\)
3 \(\mathrm{h}=0\)
4 the acceleration will be same and there is no relation between \(h\) and \(R\)
Rotational Motion

269276 When a force is applied on a body, Newton's second law is applicable to

1 center of mass
2 any part of the body
3 upper most part of body
4 lower most part of body
Rotational Motion

149749 Two particles of masses \(m_{1}\) and \(m_{2}\left(m_{1}>m_{2}\right)\), initially at rest, move towards each other under an inverse square law force of attraction. Pick out the correct statement about the centre of mass (CM) of the system

1 The CM moves towards \(m_{1}\).
2 The CM moves towards \(\mathrm{m}_{2}\).
3 The CM remains at rest.
4 The motion of CM is accelerated.
Rotational Motion

149755 A car of mass \(M\) is tied to one end of a massless rope of length \(10 \mathrm{~m}\). The other end of the rope is in the hands of a man of mass \(M\). The entire system is on a smooth horizontal surface. The man is at \(x=0\) and the cart at \(x=10 \mathrm{~m}\). If the man pulls the cart by the rope, the man and the cart will meet at the point

1 they will never meet
2 \(x=10 \mathrm{~m}\)
3 \(x=5 \mathrm{~m}\)
4 \(x=0\)
Rotational Motion

149756 Three identical metal balls each of radius \(r\) are placed touching each other on a horizontal surface such that an equilateral triangle is formed with centers of three balls joined. The centre of mass of the system is located at

1 horizontal surface
2 centre of one of the balls
3 line joining the centers of any two balls
4 point of intersection of the medians
Rotational Motion

149758 A solid sphere of radius \(R\) is placed on a smooth horizontal surface. A horizontal force \(F\) is applied at height \(h\) from the lowest point. For the maximum acceleration of the centre of mass

1 \(h=R\)
2 \(\mathrm{h}=2 \mathrm{R}\)
3 \(\mathrm{h}=0\)
4 the acceleration will be same and there is no relation between \(h\) and \(R\)
Rotational Motion

269276 When a force is applied on a body, Newton's second law is applicable to

1 center of mass
2 any part of the body
3 upper most part of body
4 lower most part of body