A block of mass m is attached to four unstretched massless springs of spring constant `k_1 and k_2` as shown in figure. The block is displaced towards right through distance x and is released. Speed of block when displacement of block is x/2 from mean position is :

Options

A. `sqrt(2(k_1 + k_2)x/m)`
B. `sqrt((3(k_1+ k_2)x^2)/(2m))`
C. `sqrt(((k_1k_2))/(3(k_1 + k_2)m))`
D. `sqrt(((k_1 + k_2)x)/((k_1 + k_2)m))`

Answer

B

Explanation

Loss in EPE = gain in KE `implies 2 {1/2 (k_1 + k_2)(x^2 - (x/2)^2)} = 1/2 mv^2 " "implies`
`v = sqrt((3(k_1 + k_2)x^2)/(2m)` .