6. 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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7. 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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8. A particle of mass M is situated at the centre of spherical shell of mass M and radius a. The magnitude of the gravitational potential at a point situated at a/2 distance from the centre, will be​​​

1. 1. 	2GM
      	a

   
   
   

   2. 	3GM
      	a

   
   
   

   3. 	4GM
      	a

   
   
   

   4. 	GM
      	a

   
   
   

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1. View Hint View Answer Discuss in Forum

   V_P = V_{spherical shell} + V_particle
   

   =	GM	=	GM	=	3GM
   	a		a / 2		a

   
   

   Correct Option: B

   V_P = V_{spherical shell} + V_particle
   

   =	GM	=	GM	=	3GM
   	a		a / 2		a

   
   

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9. Which one of the following plots represents the variation of gravitational field on a particle with distance r due to a thin spherical shell of radius R ? (r is measured from the centre of the spherical shell)
   

1. 1. 
      

   
   
   

   2. 
      

   
   
   

   3. 
      

   
   
   

   4. 

   
   
   

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1. View Hint View Answer Discuss in Forum

   The Gravitational field due to a thin spherical shell of radius R at distance r.
   

   E =	GM	(If r > R)
   	r2

   
   For   r = R i.e. on the surface of the shell
   

   E =	GM
   	R2

   
   For r < R  i.e. inside the shell ​E = 0
   

   Correct Option: B

   The Gravitational field due to a thin spherical shell of radius R at distance r.
   

   E =	GM	(If r > R)
   	r2

   
   For   r = R i.e. on the surface of the shell
   

   E =	GM
   	R2

   
   For r < R  i.e. inside the shell ​E = 0
   

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10. Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1m, 2m, 4m, 8m, ..... respectively, from the origin. The resulting gravitational potential due to this system at the origin will be​​

1. 1. -	8	G
      	3

   
   
   

   2. -	4	G
      	3

   
   
   

   3. - 4 G
      

   
   
   

   4. - G

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   Gravitational potential V =	-Gm
   	r

   
   

   V0 = -	G × 2	-	G × 2	-	G × 2	-	G × 2
   	1		2		4		8

   
   

   = -2G		1 +	1	+	1	+	1	+	1	+ .......∞
   			1		2		4		8

   
   

   = -2G ×	1				= -2G ×	1				= -4 G
   	1 -	1					1
   		2					2

   Correct Option: C

   
   

   Gravitational potential V =	-Gm
   	r

   
   

   V0 = -	G × 2	-	G × 2	-	G × 2	-	G × 2
   	1		2		4		8

   
   

   = -2G		1 +	1	+	1	+	1	+	1	+ .......∞
   			1		2		4		8

   
   

   = -2G ×	1				= -2G ×	1				= -4 G
   	1 -	1					1
   		2					2

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