Question

The mass of a metal scale of uniform thickness is $1.6kg$ and its length is $2m$. This scale is placed on the horizontal surface of the table such that ${\frac{1}{4}}^{th}$ of its length is beyond the edge of the table. The maximum mass that can be suspended to this scale at a distance of $10cm$ from the free end of the scale so that scale does not turn down is:

• A. $1kg$
• B. $2kg$
• C. $2.4kg$
• D. $3.2kg$

Answer 1

Answer: (B)

$2kg$

B is where the normal reaction N acts upward.
A is the edge of the table.
C is the point where mass m' is hung.
Equating torques due to $N=mg$ and m'g about edge A of the table,
$mg(\frac{l}{2}-\frac{l}{4})=m^{\prime }g(\frac{l}{4}-10)$ where l is the length of the scale.
Given, $l=200cm$
$\therefore m\times \frac{l}{4}=m^{\prime }(\frac{l}{4}-10)$
$\Rightarrow 1.6\times \frac{200}{4}=m^{\prime }(\frac{200}{4}-10)$
$\Rightarrow 1.6\times 50=m^{\prime }\times 40$
$\Rightarrow m^{\prime }=2kg$