Question

A vehicle is moving with a constant speed of $10\text{ m/s}$ in a circular horizontal track of radius $20\text{ m}$ . A bob is suspended from the roof of a vehicle by a massless string. The angle made by the string with the vertical will be (acceleration due to gravity, $g = 10\text{ m/s}^2$ )}

• A. $\tan^{-1}(0.5)$
• B. $\tan^{-1}(0.6)$
• C. $\tan^{-1}(0.7)$
• D. $\tan^{-1}(0.8)$

Hint:

For a bob in a turning vehicle: \[ \tan\theta=\frac{v^2}{rg} \] This is a standard circular motion result.

Answer 1

The Correct Option is A

Concept:
For a body moving in a circular path with speed \(v\) and radius \(r\), the horizontal acceleration is: \[ a_c=\frac{v^2}{r} \] For the suspended bob inside the turning vehicle: \[ \tan\theta=\frac{a_c}{g} \] ip

Step 1: Find centripetal acceleration.
\[ a_c=\frac{v^2}{r}=\frac{10^2}{20}=\frac{100}{20}=5\text{ m/s}^2 \] ip

Step 2: Use the relation for angle of deflection.
\[ \tan\theta=\frac{a_c}{g}=\frac{5}{10}=0.5 \] So, \[ \theta=\tan^{-1}(0.5) \] ip Hence, the correct answer is:
\[ \boxed{(A)\ \tan^{-1}(0.5)} \]