A body weights 8 g when placed in one pan and 18 g when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, then the true weight of the body is

Question

A body weights 8 g when placed in one pan and 18 g when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, then the true weight of the body is (A) 15 g (B) 13 g (C) 10 g (D) 12 g

Tardigrade Admin · Accepted Answer

From figure Solution

8p=wq ⇒ (p/q)=(w/8) .... (i) Now, from figure, Solution

wp=18q ⇒ (p/q)=(18/w) ..... (ii) From equations (i) and (ii), we get (p/q)=(w/8)=(18/w) w=√18 × 8=12 g

Q. A body weights $8 g$ when placed in one pan and $18 g$ when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, then the true weight of the body is

15 g

13 g

10 g

12 g

From figure

$8 p = wq$
$\Rightarrow \frac{p}{q} = \frac{w}{8}$ .... (i)
Now, from figure,

$wp = 18 q$
$\Rightarrow \frac{p}{q} = \frac{18}{w}$ ..... (ii)
From equations (i) and (ii), we get
$\frac{p}{q} = \frac{w}{8} = \frac{18}{w}$
$w = 18 \times 8 = 12 g$

Q. A body weights 8g when placed in one pan and 18g when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, then the true weight of the body is