Question

A bob of mass ${}^{\prime }{m}^{\prime }$ is attached to ceiling of a lift with the help of string as shown. Calculate tension in string in equilibrium position, when lift is accelerated forward with acceleration ${}^{\prime }{a}^{\prime }$.

• A. $m(g+a)$
• B. $m(g-a)$
• C. $m\sqrt{g^2+a^2}$
• D. $mg$

Answer 1

The correct option is C $m\sqrt{g^2+a^2}$

As lift has forward acceleration pseudo force will be backwards hence FBD is

$\Rightarrow$ here as $mg$ and $ma$ are perpendicular to each other.
Net force of $mg,ma$ is balanced by $T$
So, $T=\sqrt{(ma{)}^2+(mg{)}^2}$
$T=m\sqrt{g^2+a^2}$