A wedge of mass `M=10kg`, height h=3m and angle of inclination `alpha=37^(@)` is at rest at horizontal surface. There is a small point -like object (mass m=0.5kg) next to the slope as shown in the figure. At what acceleration musts wedge be moved in order that the point like object reaches its top in a time `t=5s (neglect the friction between point like object and wedge)

Options

A. `2m//s^(2)`
B. `4m//s^(2)`
C. `8m//s^(2)`
D. `10m//s^(2)`

Answer

C

Explanation

Let wedge is moving rightward with acceleration a and mass m has an acceleration A with respect to wedge along the surface of the wedge in upward direction, so
`(h)/(sinalpha)=(1)/(2)At^(2)impliesA=(2h)/(t^(2)sinalpha)` …(1)
With the help of FBD of mass m in the frame of wedge we can write
`A=acosalpha-gsinalphaimplies(2h)/(t^(2)sinalpha)=acosalpha-gsinalpha`
`impliesa=gtanalpha+(2h)/(t^(2)sinalphacosalpha)=10xx(3)/(4)+2xx3xx(5)/(3)xx(5)/(4)xx(1)/(5xx5)=8m//s^(2)`