The two arms of a balance are of unequal length. An object when placed in the left pan of the balance weighs 4 kg. The same object when placed in the right pan of the balance weighs 9 kg. The actual (or) true mass of the object is

Question

The two arms of a balance are of unequal length. An object when placed in the left pan of the balance weighs 4 kg. The same object when placed in the right pan of the balance weighs 9 kg. The actual (or) true mass of the object is (A) 5.5 kg (B) 6 kg (C) 6.5 kg (D) 7 kg

Tardigrade Admin · Accepted Answer

m0 l1 = m1 l2 ....(i)

m2l1 = m0 l2 ...(ii) Dividing (i) by (ii) ⇒ m02 = m1m2 ⇒ m0 = √m1m2 =√4× 9 = 6 kg

Q. The two arms of a balance are of unequal length. An object when placed in the left pan of the balance weighs $4 k g$ . The same object when placed in the right pan of the balance weighs $9 k g$ . The actual (or) true mass of the object is

$5.5 k g$

$6 k g$

$6.5 k g$

$7 k g$

$m_{0} l_{1} = m_{1} l_{2} .... (i)$

$m_{2} l_{1} = m_{0} l_{2} ... (ii)$
Dividing $(i)$ by $(ii)$
$\Rightarrow m_{0}^{2} = m_{1} m_{2}$
$\Rightarrow m_{0} = m_{1} m_{2}$
$= 4 \times 9$
$= 6 k g$

Q. The two arms of a balance are of unequal length. An object when placed in the left pan of the balance weighs 4kg. The same object when placed in the right pan of the balance weighs 9kg. The actual (or) true mass of the object is

5.5kg

6kg

6.5kg

7kg