Question

A body of mass 5 gm is executing s.H.M. About a point with amplitude 10 cm. Its maximum velocity is 100 cm/sec. Its velocity will be 50 cm/sec at a distance.

a. 5
b. 5√2
c. 5√3
d. 10√2

Answer 1

Step-by-step explanation:

Given

Amplitude
`A=10 cm`

mass of body
`m=5 gm`

maximum velocity
`v_(max)=100 cm/s`

if
`x=A\cos (\omega t)` is the general equation of SHM

where
`\omega =natural\ frequency\ of\ oscillation`

`A=maximum\ amplitude`

`t=time`

maximum amplitude is
`v_(max)=A\omega`

`100=10* \omega`

`\omega =10 cycle/s`

and velocity at any instant is given by

`v=\omega √(A^2-y^2)`

`50=10√(10^2-y^2)`

`5=√(10^2-y^2)`

squaring

`25=100-y^2`

`y^2=75`

`y=5√(3)\ cm`