Three blocks a, b and c of masses 10 kg, 10 kg and 20 kg respectively are arranged as shown in figure. All the surfaces are frictionless and string is inextensible. A constant force F = 20 N is applie

Question

Three blocks a, b and c of masses 10 kg, 10 kg and 20 kg respectively are arranged as shown in figure. All the surfaces are frictionless and string is inextensible. A constant force $F = 20$ N is applied on block a as shown. Pulleys and string are light. Part of the string connecting both pulleys is vertical and part of the strings connecting pulleys with masses a and b are horizontal.

TestHub · Accepted Answer

String constraint: the string connects block a to block b over the two pulleys mounted on c, so its length is L = (x_c - x_b) + h + (x_a - x_c) = x_a - x_b + h. Since L is constant:

$a_{a} = a_{b}$

Force equations (rightward positive):

$block a: F - T = m_{a} a_{a} \Rightarrow 20 - T = 10 a_{a}$

$block b: T = m_{b} a_{b} = 10 a_{b}$

Adding both equations (a_a = a_b):

$20 = 20 a_{b} \Rightarrow a_{b} = 1 m / s^{2}$

$T = 10 N$

Block c: the top pulley is pulled left by T and the bottom pulley is pulled right by T; all surfaces are frictionless, so the net horizontal force on c is zero:

$a_{c} = 0$

So acceleration of b is 1 m/s^2 and tension is 10 N. Correct options: (B), (C).

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