Question

A car is moving on a plane inclined at $30^{\circ }$ to the horizontal with an acceleration of $10m/s^2$ parallel to the plane upward. A bob is suspended by a string from the roof. The angle in degrees which the string makes with the vertical is: (Assume that the bob does not move relative to car) $[g=10m/s^2]$

• A. $20^{\circ }$
• B. $30^{\circ }$
• C. $45^{\circ }$
• D. $60^{\circ }$

Answer 1

Answer: (B)

In $F.B.D$. of the bob resolving the components of pseudo force and tension in horizontal and vertical direction



$Tsin\alpha =macos\theta \dots (i)$

$Tcos\alpha =masin\alpha +mg\dots (ii)$

From (i) and (ii), $tan\alpha =\frac{asin\theta }{asin\theta +g}$

Here $a=10m/s^2$,

$\theta =30^{\circ }$

After solving we get $tan\alpha =\frac{1}{\sqrt{3}}$ or $\alpha =30^{\circ }$