In an experiment with a beam balance,an unkno | vedclass

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(C) For the first case,the torque balance equation is: $16 \ell_{1} = m \ell_{2}$ (Equation $1$)For the second case,the torque balance equation is: $m

Vedclass · Accepted Answer

$8$

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(C) For the first case,the torque balance equation is: $16 \ell_{1} = m \ell_{2}$ (Equation $1$)For the second case,the torque balance equation is: $m \ell_{1} = 4 \ell_{2}$ (Equation $2$)Multiplying Equation $1$ and Equation $2$:$(16 \ell_{1}) 	imes (m \ell_{1}) = (m \ell_{2}) 	imes (4 \ell_{2})$$16 m \ell_{1}^2 = 4 m \ell_{2}^2$$4 \ell_{1}^2 = \ell_{2}^2 \Rightarrow \ell_{2} = 2 \ell_{1}$Substituting $\ell_{2} = 2 \ell_{1}$ into Equation $1$:$16 \ell_{1} = m (2 \ell_{1})$$16 = 2m$$m = 8\,kg$

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 the figure. The value of the unknown mass $m$ is ......... $kg$.

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