A body projected along an inclined plane of angle of inclination 300 stops after covering a distance `x_(1)`. The same body projected with the same speed stops after covering a distance `x_(2)` when the angle of inclination of the inclined plane is increased to `60^(@)` the ratio of `x_(1)//lx_(2)` is

Options

A. 1
B. 2
C. `sqrt2`
D. `sqrt3`

Answer

d

Explanation

`a=(F)/(m_(1)+m_(2))=(300)/(10+20)=10m//s^(2)`
Hence correct choice is (a). 51. Zz  52. Let initial speed be u and final speed in both cases
`upsilon=0,a_(1)=g sin 30^(@)=g//2`
and `a_(2) = g sin 60^(@) =(sqrt3)/(2)g`
`upsilon^(2)-u^(2)=2a_(1)x_(1)`
`implies0-u^(2)=2a_(1)x_(1)impliesx_(1)=-(u^(2))/(2a_(1))`
lily       `x_(2)=(-u^(2))/(2a_(2))`
`:.(x_(1))/(x_(2))=(a_(2))/(a_(1))=((sqrt3)/(2)g)/((1)/(2)g)=sqrt3`
Hence correct choice is (d)