1. A simple pendulum has a metal bob, which is negatively charged. If it is allowed to oscillate above a positively charged metallic plate, then its time period will​​​
   

1. 1. increase

   
   
   

   2. decrease

   
   
   

   3. become zero

   
   
   

   4. remain the same

   
   
   

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1. View Hint View Answer Discuss in Forum

   We know that the time period (T) = 2π			∝
   		l		1	g' = geffective
   		g'		√g'

   
   Since the negatively charged bob is attracted by the positively charged plate, therefore acceleration due to gravity will increase and time period will decrease.

   Correct Option: B

   We know that the time period (T) = 2π			∝
   		l		1	g' = geffective
   		g'		√g'

   
   Since the negatively charged bob is attracted by the positively charged plate, therefore acceleration due to gravity will increase and time period will decrease.

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2. The equation of a simple harmonic wave is given by
   

   y = 3 sin	π	(50 t - x)
   	2

   
   Where x and y are in meters and t is in seconds. The ratio of maximum particle velocity to the wave velocity is​​

1. 1. 2π

   
   
   

   2. 	3	π
      	2

   
   
   

   3. 3π

   
   
   

   4. 	2	π
      	3

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   y = 3 sin	π	(50 t - x)
   	2

   
   

   y = 3sin		25πt -	π	x
   			2

   
   on comparing with the standard wave equation ​y = a sin (ωt – kx) ​
   

   Wave velocity , v =	ω	=	25π	= 50 m / sec
   	k		π / 2

   
   

   The velocity of particle vp =	∂y	= 75π cos		25πt -	π	x
   	∂t				2

   
   v_pmax = 75π
   

   then	vpmax	=	75π	=	3π
   	v		50		2

   
   

   Correct Option: B

   y = 3 sin	π	(50 t - x)
   	2

   
   

   y = 3sin		25πt -	π	x
   			2

   
   on comparing with the standard wave equation ​y = a sin (ωt – kx) ​
   

   Wave velocity , v =	ω	=	25π	= 50 m / sec
   	k		π / 2

   
   

   The velocity of particle vp =	∂y	= 75π cos		25πt -	π	x
   	∂t				2

   
   v_pmax = 75π
   

   then	vpmax	=	75π	=	3π
   	v		50		2

   
   

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