Question

A small meitalic sphere of mass m is suspended from the ceiling of a car accelerating on a horizontal and with constant acceleration a. The tension in the string attached with metalic 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 $m\sqrt{g^2+a^2}$

Since, there is movement of the car, the string will accelerate thereby making some angles . let $\theta$ be the angles made by the string while moving from its original position to displaced position. On resolving the tension T, when it makes since and cosine components.

Vertical component is given by ,

$\begin{array}{c}T\cos \theta =mg---\left(1\right)\\ Horizontalcomponentis\\ T\sin \theta =ma---\left(2\right)\\ Squaringandadding\left(1\right)+\left(2\right).\\ T^2{\cos }^2\theta +T^2{\sin }^2\theta =m^2{a}^2+m^2{g}^2\\ T^2\left({\cos }^2\theta +{\sin }^2\theta \right)=m^2\left(a^2+g^2\right)\\ T^2=m^2\left(a^2+g^2\right)\\ T=m\sqrt{\left(a^2+g^2\right)}\\ Hence,optionDisthecorrectanswer.\end{array}$