1. ​The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2m on the surface of A. What is the height of jump by the same person on the planet B?​​
   

1. 1. 	2	m
      	3

   
   
   

   2. 	2	m
      	9

   
   
   

   3. 18 m
      

   
   
   

   4. 6 m

   
   
   

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1. View Hint View Answer Discuss in Forum

   Applying conservation of total mechanical energy principle
   

   	1	mv2 = mgAhA = mgBhB
   	2

   
   ⇒ g_A h_A = g_B h_B
   

   ⇒ hB =		gA		hA = 9 × 2 = 18 m
   		gB

   
   

   Correct Option: C

   Applying conservation of total mechanical energy principle
   

   	1	mv2 = mgAhA = mgBhB
   	2

   
   ⇒ g_A h_A = g_B h_B
   

   ⇒ hB =		gA		hA = 9 × 2 = 18 m
   		gB

   
   

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2. In a rocket a seconds pendulum is mounted. Its period of oscillation decreases when the rocket
   

1. 1. comes down with uniform acceleration ​

   
   
   

   2. moves  round the earth  in a geostationary orbit

   
   
   

   3. moves up with a uniform velocity ​

   
   
   

   4. moves up with uniform acceleration

   
   
   

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1. View Hint View Answer Discuss in Forum

   T = 2π √l / g .When the rocket accelerates upwards g increases to ( g + a).

   Correct Option: D

   T = 2π √l / g .When the rocket accelerates upwards g increases to ( g + a).

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3. A body weighs 72 N on the surface of the earth. What is the gravitational force on it due to earth at a height equal to half the radius of the earth from the surface?​​​
   

1. 1. 32 N

   
   
   

   2. 28 N

   
   
   

   3. ​16 N

   
   
   

   4. 72 N

   
   
   

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1. View Hint View Answer Discuss in Forum

   mg = 72 N  (body weight on the surface)
   

   g =	GM
   	R2

   
   

   At a height H =	R
   	2

   
   

   g' =	GM					-	4 GM
   		R +	R		2		9R2
   			2

   
   

   Body weight at height H =	R
   	2

   
   

   mg' = m ×	4		GM
   	9		R2

   
   

   = m ×	4	× g =	4	mg
   	9		9

   
   

   =	4	× 72 = 32 N
   	9

   
   

   Correct Option: A

   mg = 72 N  (body weight on the surface)
   

   g =	GM
   	R2

   
   

   At a height H =	R
   	2

   
   

   g' =	GM					-	4 GM
   		R +	R		2		9R2
   			2

   
   

   Body weight at height H =	R
   	2

   
   

   mg' = m ×	4		GM
   	9		R2

   
   

   = m ×	4	× g =	4	mg
   	9		9

   
   

   =	4	× 72 = 32 N
   	9

   
   

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4. Assuming earth to be a sphere of uniform density, what is the value of ‘g’ in a mine 100 km below the earth’s surface? (Given, R = 6400 km)
   

1. 1. 9.65 m / s²
      

   
   
   

   2. 7.65 m / s²
      

   
   
   

   3. 5.06 m / s²
      

   
   
   

   4. 3.10 m / s²

   
   
   

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1. View Hint View Answer Discuss in Forum

   We know that effective gravity g' at depth  below earth surface is given by
   

   g' = g		1 -	d
   			R

   
   Here, d = 100 km, R = 6400 km,
   

   ∴ g' = 9.8		1 -	100		= 9.65 m / s2
   			6400

   Correct Option: A

   We know that effective gravity g' at depth  below earth surface is given by
   

   g' = g		1 -	d
   			R

   
   Here, d = 100 km, R = 6400 km,
   

   ∴ g' = 9.8		1 -	100		= 9.65 m / s2
   			6400

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5. At what height from the surface of earth the gravitational potential and the value of g are –5.4 × 10⁷ J kg^–1 and 6.0 ms^–2 respectively ? ​Take the radius of earth as 6400 km :​
   

1. 1. 2600 km

   
   
   

   2. ​1600 km

   
   
   

   3. ​1400 km

   
   
   

   4. 2000 km

   
   
   

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1. View Hint View Answer Discuss in Forum

   As we know, gravitational potential (v) and acceleration due to gravity (g) with height
   

   V =	-GM	= -5.4 × 107 ......(1)
   	R + h

   
   

   and g =	-GM	= 6 ........(2)
   	(R + h)2

   
   Dividing (1) by (2)
   

   		-GM
   		R + h		=	-5.4 × 107
   		GM			6
   		(R + h)2

   
   

   ⇒	5.4 × 107	= 6
   	(R + h)

   
   ⇒​R + h = 9000 km so, h = 2600 km
   

   Correct Option: A

   As we know, gravitational potential (v) and acceleration due to gravity (g) with height
   

   V =	-GM	= -5.4 × 107 ......(1)
   	R + h

   
   

   and g =	-GM	= 6 ........(2)
   	(R + h)2

   
   Dividing (1) by (2)
   

   		-GM
   		R + h		=	-5.4 × 107
   		GM			6
   		(R + h)2

   
   

   ⇒	5.4 × 107	= 6
   	(R + h)

   
   ⇒​R + h = 9000 km so, h = 2600 km
   

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