Answer to Question #87902 in Classical Mechanics for Anurag

Question

A small ball is suspended from a thread. It is lifted up with an acceleration 4.9 ms(sq) and lowered with an acceleration 4.9ms(sq) then the ratio of tensions in the thread in both cases will be :-

Answer 1

Earth gravitational acceleration: $g=9.8 \, \text{ms}^{-2}$

When a small ball is lifted up with an acceleration $a=4.9 \, \text{ms}^{-2}$ , the tension of the thread equals to

$$T_u=m(g+a)$$

When it is lowered with the same acceleration, , the tension of the thread equals to

$$T_d=m(g-a)$$

The ratio:

$$\frac{T_u}{T_d} = \frac{g+a}{g-a}=\frac{9.8+4.9}{9.8-4.9}=3$$