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A small ball is kept on the top of a sph...

A small ball is kept on the top of a sphere of radius `R`. The sphere start accelerating with constant acceleration of `10m//s^(2)` horizontally. The angle of radial line with the vertical at which small ball leaves the sphere is `1/2 sin^(-1)(K//9)`. Find the value of `K`. [take `g=10m//s^(2)`]

A

4

B

2

C

1

D

0.5

Text Solution

Verified by Experts

The correct Answer is:
A
(a) Since, the cube is half immersed. The density of cube should be half the density of water, i.e., `500 kgm^(-3)`
`T=2pisqrt((m)/(rho_(u)Ag)) " "(k=rho_(u)Ag)`
`(pi)/(5)=2pisqrt((a^(3)xx rho)/(rho_(w)xx a^(2) xx g))`
`therefore (arho)/(grho_(w))=(1)/(100)`
`therefore (a)/(20)=(1)/(100)` or a=(0.2)m
Now, `m=a^(3)rho=4 kg" "`(`because` Mass =Density `xx` Volume)
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