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Q.

A body of mass 10 kg is kept at a height of 10m from the ground. When it is released after some time, its kinetic energy becomes 450J. Which of the following will be the potential energy of the body at that instant?

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a

650J

b

550J

c

450J

d

350J

answer is B.

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Detailed Solution

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Potential energy is the amount of energy stored in an object due to its position.
The potential energy of the object decreases as it approaches the ground, while the kinetic energy increases.
We have,

Potential Energy = mgh

Kinetic energy = 12×m×v2
Given:
Mass, m = 10 kg

height = 10 m
At a height of 10m the mechanical energy of the body, 

E = Kinetic energy + Potential energy

E=12×m×v2+mgh
E =12×10×(0)2+10×10×10       (initial velocity of the body is zero) 
E=10×10×10=1000 joule 

We are given that after some time the kinetic energy is 450J.
Suppose at that instant potential energy is u, then by the law of conservation of mechanical energy 
E = 450 + u

1000 = 450 + u
⇒ u = 1000 - 450

⇒ u = 550J
 The potential energy of the body at that instant is given by 550J.

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