Two blocks of masses 0.25 kg and 0.80 kg are connected by means of a light inextensible string that goes over a smooth and massless pulley. What is the work done (in joules) by string on the 0.25 kg block during the first second of its motion after being released from rest? (Take `g = 10 ms^(-2)`)

Answer

`09.98`

Explanation

Acceleration is given by,
`a = ("Net pulling force")/("Total mass") = (0.80 g - 0.25 g)/(0.80 + 0.25) = (1 g)/21`
Displacement is given by:
`s = 1/2 at^(2) = 1/2 ((11 g)/21) (1)^(2) = (11 g)/42`

Balancing force, we get
`T -0.25 g = 0.25 a`
`therefore T = 1/4 g 1/4 ((11g)/21)`
`therefore T = 8/21 g`
Now, for 0.25 kg mass,
`W_(T) = T cos 0^(@) = 8/21 g xx 111/42 g xx I = 44/441 (g^(2))`
`therefore W_(T) = 9.98 J`