Question

When the trolley shown in figure is given a horizontal acceleration $a$, the pendulum bob of mass $m$ gets deflected to a maximum angle $\theta$ with the vertical. At the position of maximum deflection, the net acceleration of the bob with respect to trolley is

• A. $\sqrt{g^2+a^2}$
• B. $a\cos \theta$
• C. $g\sin \theta -a\cos \theta$
• D. $a\sin \theta$

Answer 1

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

Constructing F.B.D of Bob with respect to trolley is

$F_{net}=\sqrt{m^2{g}^2+m^2{a}^2}$

$F_{net}=ma$

$M\sqrt{g^2+a^2}=M{a}_{res}$

$a_{Res}=\sqrt{g^2+a^2}$