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The potential energy of a body is given ...

The potential energy of a body is given by `U = A - Bx^(2)` (where x is the displacement). The magnitude of force acting on the partical is

A

constant

B

proportional to `x^(2)`

C

proportional to x

D

inversely proportional to x

Text Solution

Verified by Experts

The correct Answer is:
C

At A , the total energy of the ball `E_A=mgh_1`
`(:'K.E.=0)`
At B, it has only K.E. but it loses some energy hence the ball rises only upto a high `h_2` and P.E at C=`mgh_2`
`:.` Loss in energy=`mg(h_1-h_2)`
`:.` Percentage loss of energy
`[(mg(h_1-h_2))/(mgh_1)]xx100`
`=((h_1h_2)/(h_1))xx100=((2-1.5)/(2))xx100`
`1/4xx100=25%`
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