31. A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 seconds in every circular loop. The average velocity and average speed for each circular loop respectively, is
    

1. 1. 0, 10 m/s

   
   
   

   2. 10 m/s, 10 m/s

   
   
   

   3. 10 m/s, 0

   
   
   

   4. 0, 0

   
   
   

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1. View Hint View Answer Discuss in Forum

   Distance covered in one circular loop = 2πr ​
   = 2 × 3.14 × 100 = 628 m ​
   

   Speed =	628	= 10 m / sec
   	62.8

   
   Displacement in one circular loop = 0 ​
   

   Velocity =	0	= 0
   	time

   
   

   Correct Option: A

   Distance covered in one circular loop = 2πr ​
   = 2 × 3.14 × 100 = 628 m ​
   

   Speed =	628	= 10 m / sec
   	62.8

   
   Displacement in one circular loop = 0 ​
   

   Velocity =	0	= 0
   	time

   
   

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32. A boat is sent across a river with a velocity of 8 km h^–1. If the resultant velocity of boat is 10 km h^–1 , then the velocity of the river is
    

1. 1. 12.8 km h^–1

   
   
   

   2. 6 km h^–1

   
   
   

   3. 8 km h^–1

   
   
   

   4. 10 km h^–1

   
   
   

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1. View Hint View Answer Discuss in Forum

   v_r = √v_R² - v_B² = √10² - 8² = 6 km h^-1

   Correct Option: B

   v_r = √v_R² - v_B² = √10² - 8² = 6 km h^-1

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33. When a body moves with a constant speed along  a circle
    

1. 1. ​its velocity remains constant ​

   
   
   

   2. ​no force acts on it

   
   
   

   3. no work is done on it ​

   
   
   

   4. no acceleration is produced in it

   
   
   

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1. View Hint View Answer Discuss in Forum

   On circular motion, the force acts along the radius and displacement at a location is perpendicular to the radius i.e., θ = 90° ​As work done = F^→ . S^→ = FS cos 90° = 0
   

   Correct Option: C

   On circular motion, the force acts along the radius and displacement at a location is perpendicular to the radius i.e., θ = 90° ​As work done = F^→ . S^→ = FS cos 90° = 0
   

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34. A body is whirled in a horizontal circle of radius 20 cm. It has an angular velocity of 10 rad/s. What is its linear velocity at any point on circular path​​
    

1. 1. √2 m / s

   
   
   

   2. 2 m / s ​

   
   
   

   3. 10 m / s

   
   
   

   4. 20 m / s

   
   
   

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1. View Hint View Answer Discuss in Forum

   Radius of circular path = 20 cm =	2	m
   	10

   
   Angular speed of body = 10 rad/s ​
   Linear velocity = radius × Angular speed
   

   =	2	× 10 = 2 m / s
   	10

   Correct Option: B

   Radius of circular path = 20 cm =	2	m
   	10

   
   Angular speed of body = 10 rad/s ​
   Linear velocity = radius × Angular speed
   

   =	2	× 10 = 2 m / s
   	10

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35. A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved?​​​
    

1. 1. 14 m/s

   
   
   

   2. 3 m/s

   
   
   

   3. 5 m/s

   
   
   

   4. 3.92 m/s

   
   
   

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1. View Hint View Answer Discuss in Forum

   T =	mv2
   	R

   
   

   Correct Option: A

   T =	mv2
   	R

   
   

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