A block of mass 1 kg and density `0.8g//cm^(3)` is held stationary with the help of a string as shown in figure. The tank is accelerating vertically upwards with an acceleration a `=1.0m//s^(2)`. Find

(a) the tension in the string,
(b) if the string is now cut find the acceleration of block.
(Take `g=10m//s^(2)` and density of water `=10^(3)kg//m^(3))`.

Answer

A, B, C

Explanation

(a) Free body diagram of the block is shown in figure.
In the Figure

`F=`upthrust force
`=Vrho_(w)(g+a)`
`=(("mass of block")/("density of block"))rho_(w)(g+a)`
`=((1)/(800))(1000)(10+1)=13.75 N`
`w=mg=10N`
Equation of motion of the block is,
`F-T-w=ma`
`:. T=2.75N`.
(b) When the string is cut, `T=0 `
`a=(F-w)/(m)`
`=(13.75-10)/(1)`
`=3.75 m//s^(2)`.