1. A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98 × 10²⁴ kg) have to be compressed to be a black hole?​​​
   

1. 1. 10^–9 m

   
   
   

   2. ​10^–6 m

   
   
   

   3. ​10^–2 m

   
   
   

   4. 100 m

   
   
   

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1. View Hint View Answer Discuss in Forum

   From question, ​Escape velocity = √2GM / R = c = speed of light
   

   ⇒ R =	2GM
   	c2

   
   

   =	2 × 6.6 × 10-11 × 5.98 × 1024	= 10-2 m
   	(3 × 108)2

   Correct Option: C

   From question, ​Escape velocity = √2GM / R = c = speed of light
   

   ⇒ R =	2GM
   	c2

   
   

   =	2 × 6.6 × 10-11 × 5.98 × 1024	= 10-2 m
   	(3 × 108)2

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2. ​The height at which the weight of a body becomes 1/16th, its weight on the surface of earth (radius R), is :​​​
   

1. 1. 5R

   
   
   

   2. 15R

   
   
   

   3. 3R

   
   
   

   4. 4R

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let at h height, the weight of a body becomes	1	th of its weight on the surface.
   	16

   ​​​
   W_h = 16 W_s....(i) ​
   ⇒​16 W_s = W_s​....(ii)
   

   g' =	G M
   	(Re + h)2

   
   

   Similarly , g =	G M
   	Re2

   
   

   	g'	=	Re2	⇒ g' = g		1 +	h		-2
   	g		(Re + h)2				R

   
   ⇒ W_h = 16 W_s
   

   g' =	g
   	16

   
   

   g' = 16g		1 +	h		2
   			R

   
   

   	1	=		1 +	h		-2	⇒ 4 = 1 +	h
   	16				R				R

   
   h = 3R
   

   Correct Option: C

   Let at h height, the weight of a body becomes	1	th of its weight on the surface.
   	16

   ​​​
   W_h = 16 W_s....(i) ​
   ⇒​16 W_s = W_s​....(ii)
   

   g' =	G M
   	(Re + h)2

   
   

   Similarly , g =	G M
   	Re2

   
   

   	g'	=	Re2	⇒ g' = g		1 +	h		-2
   	g		(Re + h)2				R

   
   ⇒ W_h = 16 W_s
   

   g' =	g
   	16

   
   

   g' = 16g		1 +	h		2
   			R

   
   

   	1	=		1 +	h		-2	⇒ 4 = 1 +	h
   	16				R				R

   
   h = 3R
   

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3. A satellite A of mass m is at a distance of r from the surface of the earth. Another satellite B of mass 2m is at a distance of 2r from  the earth’s centre. Their time periods are in the ratio of​​​
   

1. 1. 1 : 2

   
   
   

   2. 1 : 16

   
   
   

   3. 1 : 32

   
   
   

   4. ​1 : 2 √2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Time period does not depend on the mass.
   Also, T² ∝ r³ .

   Correct Option: D

   Time period does not depend on the mass.
   Also, T² ∝ r³ .

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