First slide

Connected bodies

Question

Two weights W₁ and W₂ are attached to the ends of a string which passes over a frictionless pulley. If the pulley is placed in a rocket accelerating upwards at 9.8 m/s², the tension in the string would be (take g = 9.8 m/s²)

Moderate

A

$4 (\frac{W_{1} W_{2}}{W_{1} + W_{2}})$
B

$2 (\frac{W_{1} W_{2}}{W_{1} + W_{2}})$
C

$(\frac{W_{1} W_{2}}{W_{1} + W_{2}})$
D

$(\frac{W_{1} W_{2}}{W_{1} - W_{2}})$

Solution

See fig.
Tension in the string
$\begin{aligned} T & = (\frac{2 m_{1} m_{2}}{m_{1} + m_{2}}) g \\ = \frac{2 (m_{1} g) (m_{2} g)}{m_{1} g + m_{2} g} = \frac{2 W_{1} W_{2}}{W_{1} + W_{2}} \end{aligned}$
When the pulley is accelerating upwards accelerating, each weight is doubled.
$∴ T^{'} = \frac{2 (2 W_{1}) (2 W_{2})}{(2 W_{1}) + (2 W_{2})} = \frac{4 W_{1} W_{2}}{W_{1} + W_{2}}$

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