In an experiment with a beam balance, an unknown mass $m$ is balanced by two known masses of $16 k g$ and $4 k g$ as shown in fig. Find $m$ .

10 k g

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6 k g

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8 k g

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12 k g

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Solution

The correct option is D $8 k g$
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)
$\frac{m}{16} = \frac{4}{m}$
$\Rightarrow m^{2} = 64$
$\Rightarrow m = 8$

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In an experiment with a beam balance, an unknown mass m is balanced by two known masses of 16 kg and 4 kg as shown in fig. Find m.

The correct option is D 8 kgHere we can balance torque about wedge point as follows16l1=l2m ⇒l1l2=m16 ....(1)ml1=4l2 ⇒l1l2=4m ....(2)From (1) and (2)m16=4m⇒m2=64⇒m=8

In an experiment with a beam balance, an unknown mass $m$ is balanced by two known masses of $16 k g$ and $4 k g$ as shown in fig. Find $m$ .