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An object of mass m is tied to a string ...

An object of mass `m` is tied to a string of length `l` and a variable force F is applied on it which brings the string gradually at angle `theta` with the vertical. Find the work done by the force `F`.
.

A

`mgl(1+costheta)`

B

`(mg)/(l(1-costheta))`

C

`mgl(1-costheta)`

D

`(mg)/(l(1+costheta))`

Text Solution

Verified by Experts

The correct Answer is:
C
In this case, three forces are acting on the object:
1. tension (T)
2. weight (mg) and
3. applied force (F)
Using work-enegy theorem
(##DCP_V01_C09_S01_010_S01##).
`W _ (n et)=DeltaKE`
or `W_(T) + W_(mg) + W_(F)=0` ...(i)
as `DeltaKE=0`
because `K_(i) = K_(f) = 0`
Further, `W_T=0,` . as tension is always perpendicular to displacement.
`W_(mg) =-mgh`
or `w_(mg)=-mgl(1-costheta)`
Substituting these values in Eq. (i), we get
`W_(F) = mgl(1-costheta)`.
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