36. A person swims in a river aiming to reach exactly opposite point on the bank of a river. His speed of swimming is 0.5 m/s at an angle 120° with the direction of flow of water. The speed of water in stream is​​​
    

1. 1. ​1.0 m/s ​

   
   
   

   2. 0.5 m/s

   
   
   

   3. 0.25 m/s ​

   
   
   

   4. 0.43 m/s.

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   Velocity of person v^→_m = 0.5 m/s
   

   sin 30° =	vw	⇒ vw = vm sin 30°
   	vm

   
   

   ⇒ vw =	vm	=	0.5 m / s	= 0.25 m / s
   	2		2

   
   

   Correct Option: C

   
   Velocity of person v^→_m = 0.5 m/s
   

   sin 30° =	vw	⇒ vw = vm sin 30°
   	vm

   
   

   ⇒ vw =	vm	=	0.5 m / s	= 0.25 m / s
   	2		2

   
   

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37. A stone tied with a string, is rotated in a vertical circle. The minimum speed with which the string has to be rotated​​​
    

1. 1. ​is independent of the mass of the stone ​

   
   
   

   2. ​is independent of the length of the string ​

   
   
   

   3. decreases with increasing mass of the stone ​

   
   
   

   4. ​decreases with increasing length of the string

   
   
   

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1. View Hint View Answer Discuss in Forum

   Minimum speed with which the string is rotating in a vertical circle (v) = ​√gr
   The minimum speed of stone is independent of mass of stone.

   Correct Option: A

   Minimum speed with which the string is rotating in a vertical circle (v) = ​√gr
   The minimum speed of stone is independent of mass of stone.

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38. A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is​
    

1. 1. 3
      

   
   
   

   2. 4
      

   
   
   

   3. √21
      

   
   
   

   4. 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   Speed along the shortest path
   

   	1	= 4 km / hr
   	15 / 60

   
   Speed of water v = √5² - 4² = 3 km / hr
   

   Correct Option: A

   
   Speed along the shortest path
   

   	1	= 4 km / hr
   	15 / 60

   
   Speed of water v = √5² - 4² = 3 km / hr
   

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39. A small sphere is attached to a cord and rotates in a vertical circle about a point O. If the average speed of the sphere is increased, the cord is most likely to break at the orientation when the mass is at
    
    

1. 1. bottom point B ​

   
   
   

   2. the point C ​

   
   
   

   3. ​the point D ​

   
   
   

   4. top point A

   
   
   

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1. View Hint View Answer Discuss in Forum

   In the case of a body describing a vertical circle,
   
   

   T - mg cosθ =	mv2	; T = mg cosθ -	mv2
   	l		l

   
   Tension is maximum when cos θ = + 1 and velocity is maximum ​
   Both conditions are satisfied at θ = 0° (i.e. at lowest point B)

   Correct Option: A

   In the case of a body describing a vertical circle,
   
   

   T - mg cosθ =	mv2	; T = mg cosθ -	mv2
   	l		l

   
   Tension is maximum when cos θ = + 1 and velocity is maximum ​
   Both conditions are satisfied at θ = 0° (i.e. at lowest point B)

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40. Two particles of mass M and m are moving in a circle of radii R and r. If their time-periods are same, what will be the ratio of their linear velocities?​​​
    

1. 1. MR : mr

   
   
   

   2. M : m ​

   
   
   

   3. R : r

   
   
   

   4. ​1 : 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   ​Linear velocity v = rω ​
   v₁ = ωr₁, v₂ = ωr₂ ​
   [ω is same in both cases because time period is same]
   

   	v1	=	r1	=	R
   	v2		r2		r

   
   

   Correct Option: C

   ​Linear velocity v = rω ​
   v₁ = ωr₁, v₂ = ωr₂ ​
   [ω is same in both cases because time period is same]
   

   	v1	=	r1	=	R
   	v2		r2		r

   
   

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