16. Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be:

1. 1. 2v

   
   
   

   2. zero

   
   
   

   3. 1.5

   
   
   

   4. v

   
   
   

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1. View Hint View Answer Discuss in Forum

   If no external force actson a system of particles, the centre of mass remains at rest. So, speed of centre of mass is zero.

   Correct Option: B

   If no external force actson a system of particles, the centre of mass remains at rest. So, speed of centre of mass is zero.

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17. Three masses are placed on the x-axis : 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70 cm. The distance of the centre of mass from the origin is :

1. 1. 40 cm

   
   
   

   2. 45 cm

   
   
   

   3. 50 cm

   
   
   

   4. 30 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   Xcm =	m1x1 + m2x2 + m3x3
   	m1 + m2 + m3

   
   

   Xcm =	300 × (0) + 500 × (40) + 400 × (70)
   	300 + 500 + 400

   
   

   Xcm =	500 × 40 + 400 × 70
   	1200

   
   

   Xcm =	50 + 70	=	120	= 40 cm
   	3		3

   Correct Option: A

   Xcm =	m1x1 + m2x2 + m3x3
   	m1 + m2 + m3

   
   

   Xcm =	300 × (0) + 500 × (40) + 400 × (70)
   	300 + 500 + 400

   
   

   Xcm =	500 × 40 + 400 × 70
   	1200

   
   

   Xcm =	50 + 70	=	120	= 40 cm
   	3		3

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18. Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weighs 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water the centre of mass of the system shifts by :

1. 1. 3.0 m

   
   
   

   2. 2.3 m

   
   
   

   3. zero

   
   
   

   4. 0.75 m

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   There is no external force so centre of mass of the system will not shift

   Correct Option: C

   
   There is no external force so centre of mass of the system will not shift

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19. The moment of inertia of a disc of mass M and radius R about an axis, which is tangential to the circumference of the disc and parallel parallel to its diameter, is

1. 1. 3	MR²
      2

   
   
   

   2. 2	MR²
      3

   
   
   

   3. 5	MR²
      4

   
   
   

   4. 4	MR²
      5

   
   
   

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1. View Hint View Answer Discuss in Forum

   Moment of inertia of disc about its diameter is
   

   Id =	1	MR²
   	4

   
   
   MI of disc about a tangent passing through rim and in the plane of disc is
   

   I = Id + MR² =	1	MR² + MR² =	5	MR²
   	4		4

   Correct Option: C

   Moment of inertia of disc about its diameter is
   

   Id =	1	MR²
   	4

   
   
   MI of disc about a tangent passing through rim and in the plane of disc is
   

   I = Id + MR² =	1	MR² + MR² =	5	MR²
   	4		4

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20. The speed of a homogenous solid sphere after rolling down an inclined plane of vertical height h from rest without sliding is

1. 1. √	10	gh
      	7

   
   
   

   2. √gh

   
   
   

   3. √	6	gh
      	5

   
   
   

   4. √	4	gh
      	3

   
   
   

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1. View Hint View Answer Discuss in Forum

   P.E. = total K.E.
   

   mgh =	7	mv²
   	10

   
   

   ∴ v = √	10 gh	mv²
   	7

   Correct Option: A

   P.E. = total K.E.
   

   mgh =	7	mv²
   	10

   
   

   ∴ v = √	10 gh	mv²
   	7

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