In an experiment with a beam balance on unknown mass m is balanced by two known mass m is balanced b

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6.System of Particles and Rotational Motion

hard

In an experiment with a beam balance on unknown mass $m$ is balanced by two known mass $m$ is balanced by two known masses of $16\, kg$ and $4\, kg$ as shown in figure. The value of the unknown mass $m$ is ....... $kg$.

A

$10$

B

$6$

C

$8$

D

$12$

Solution

Here we can balance torque about wedge point as follows

$16 l_{1}=l_{2} m \Rightarrow \frac{l_{1}}{l_{2}}=\frac{m}{16}$$…(1)$

$m l_{1}=4 l_{2} \Rightarrow \frac{l_{1}}{l_{2}}=\frac{4}{m}$$…(2)$

From $(1)$ and $( 2)$

$\frac{m}{16}=\frac{4}{m}$

$\Rightarrow m^{2}=64$

$\Rightarrow m=8$

Standard 11

Physics

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