Question

A small metallic sphere of mass $m$ is suspended from the ceiling of a car accelerating on a horizontal road with constant acceleration $a$ as shown in the figure. The tension in the string attached with the metallic sphere is

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

Answer 1

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

The given system can be reframed as shown

So, from the figure we have equation of force as
$T\cos \theta =mg$ ... (i)
$T\sin \theta =ma$ ... (ii)
Square and add (i) and (ii)
$\Rightarrow T=m\sqrt{a^2+g^2}$