JEE Main · 2021 · 31 Aug 2021 · Shift 1 · Laws of Motion

In the car's frame the bob feels gravity $g$ downward and a pseudo-acceleration $a$ directed down the incline. Resolving the pseudo-acceleration, its horizontal part is $a\cos 30^{\circ }=5\sqrt{3}\mathrm{m}{\mathrm{s}}^{-2}$ and its downward vertical part is $a\sin 30^{\circ }=5\mathrm{m}{\mathrm{s}}^{-2}$. The string lines up with the net effective gravity, whose horizontal component is $5\sqrt{3}$ and whose vertical component is $g+a\sin 30^{\circ }=15\mathrm{m}{\mathrm{s}}^{-2}$. Thus giving $\theta =30^{\circ }$.