A solid sphere of mass `m=2 kg` and density `rho=500kg//m^(3)` is held stationary relative to a tank filled with water. The tank is acceerating upward with acceleration `2m//s^(2)`. Calculate
(a) Tension in the thread connected between the sphere and the bottom of the tank.
(b) If the thread snaps, calculate the acceleration of sphere with respect to the tank. (Density of water`=1000kg//m^(3),g=10m//s^(2))`

Answer

A, B, D

Explanation

(a) Upthrust-weight -T=ma
`:. T=Upthrust - Weight-ma`
`=((2)/(500))(1000)(10+2)-20-4`
`=48-20-4=24N`
(b) Downward force T suddenly becomes zero. Therefore
`a=("upthrust-weight")/(m)=(48-20)/(2)`
`=14mm//s^(2)`
`:.` Acceleration w.r.t. tank
`=14-2`
`=12m//s^(2)`