The potential energy of a long spring when stretched by 2cm is U. If the spring is stretched by 8 cm the potential energy stored in it is……….

Options

A. `8U`
B. `16U`
C. `(U)/(4)`
D. `4U`

Answer

B

Explanation

Potential energy stored in spring `U= (1)/(2) kx^(2)`
For `x=2, U= (1)/(2)k(2)^(2)= 4xx (k)/(2)= 2k" ""……"(1)`
For `x=8 cm," new "U= U.= (1)/(2) k(8)^(2)= (1)/(2)k(64)`
`= 32k= 16(2k)`
`therefore U.= 16U" "therefore " from equation (1) ")`