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  4. A mass of 1 kg is suspended by means of a thread. The system is (i) lifted up with an acceleration of 4.9 m s-2 (ii) lowered with an acceleration of 4.9 m s-2 . The ratio of tension in the first and second case is

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Q. A mass of $1 \,kg$ is suspended by means of a thread. The system is
(i) lifted up with an acceleration of $4.9 \,m$ $s^{-2}$
(ii) lowered with an acceleration of $4.9 \,m$ $s^{-2}$ .
The ratio of tension in the first and second case is

AIPMTAIPMT 1998Laws of Motion

Solution:

Upward acceleration, $m a=T_{1}-m g$
$T_{1}=m(g+a)$
Downward acceleration, $m a=m g-T_{2}$
or, $T_{2}=m(g-a)$
$\frac{T_{1}}{T_{2}}=\frac{g+a}{g-a}=\frac{9.8+4.9}{9.8-4.9}=3: 1 \text {. }$