From the fixed pulley, masses 2 kg, 1 kg and 3 kg are suspended as shown is figure. Find the extension in the spring when acceleration of 3 kg and 1 kg is same if spring constant of the spring k = 100 N/m. (Take `g = 10 ms^(-2)`)

Options

A. (a)10 cm
B. (b)20 cm
C. (c)30 cm
D. (d)25 cm

Answer

B

Explanation

T - 20 = 20….(i) 10 + kx - T = a …(2) 30 - kx = 3a …..(3)
Adding all the equation 10 + 30 - 20 a `implies (10)/(3) m//s^(2)`
`implies x = (30 - 3a)/(k) = (30 - 3 xx (10)/(3))/(100) = (20)/(100) n`