Question

A body of mass $40kg$ stands on a weighing machine in an acceleration lift. The reading on the scale of the weighing machine is $300N$. Find the magnitude and direction of acceleration.

• A. $2.75m/s^2$ upwards
• B. $2.3m/s^2$ downwards
• C. $4.6m/s^2$ upwards
• D. $4.6m/s^2$ downwards

Answer 1

The correct option is B $2.3m/s^2$ downwards

Given :- Mass of the body $=m_1=40kg$

Weight $=300N$

The reading in weighing machine is $300N$

$\therefore$ The mass shown on weighing machine is calculated as,

$w=m_{2}g$

$\therefore 300=m_2\times 9.8$

$\therefore m_2=30.61kg$

The mass $\left(m_2\right)$ shows that it is less than the actual mass $\left(m_1\right)$ of the body, Therefore the mass is decreased, hence we say that the lift is accelerating downwards direction. Because the weight decrease when lift is moving downwards.

$\therefore$ The Tension in cable when lift is accelerating downwards is,

$\therefore T=m_{1}g-m_{1}a$

$T=m_1(g-a)$

$\therefore 300=40(9.8-a)$

$\therefore \frac{300}{40}=9.8-a$

$\therefore a=9.8-\frac{15}{2}$

$\therefore a=2.3m/s^2$

$\therefore$ Lift is accelerating downwards with acceleration

$\therefore$ Option $B$ is correct.