Question

Spring P has force constant k and a little boy stretches it a distance ℓ. Spring Q has force constant 2 k and the same little boy stretches it a distance 2 ℓ. What is the ratio WQ WP of the work done by the boy?

Answer 1

`(W_Q)/(W_P)={8}`

Step-by-step explanation:

For spring P

Spring constant = k

Stretches length = l

The work done by boy

`W_P=(1)/(2)kl^2`

For spring Q

Spring constant = 2k

Stretches length =2 l

The work done by boy

`W_Q=(1)/(2)2k(2l)^2`

`W_Q=(1)/(2)* 8kl^2`

From above equation we can say that

`(W_P)/(W_Q)=((1)/(2)kl^2)/((1)/(2)* 8kl^2)`

`(W_P)/(W_Q)=(1)/(8)`

`(W_Q)/(W_P)={8}`