In the system shown in the figure, the acceleration of 1 kg block is

Options

A. `(g)/(2)` downwards
B. `(g)/(2)` upwards
C. `(g )/(4)` downwards
D. `(g)/(4)` upwards

Answer

B

Explanation

IF a is the downward acceleration of 4 kg block the upward acceleration of 1 kg block must be 2a . If T is the tension in each part of string , then the equation of motion of 4 kg block is
` 4g - 2T = 4a ` … (I )
and the equation of motion of 1kg block is
` T- 1g=1 (2a)`
Multiplying eqn . (ii) by 2 we , get
`2T - 2g = 4a `
Adding eqs (i ) and (iii) we get
` 2 g = 8a or a=(2)/(8) = (g)/(4)`
` therefore ` The acceleration of ` 1 kg ` block
`= 2a =2 ((g)/(4) = (g)/(2) ` upwards