Question 191: Work, Energy and Power & Circular Motion

Question

A vehicle is moving with a constant speed of $10 \mathrm{~m} / \mathrm{s}$ in a circular horizontal track of radius 20 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, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

Accepted Answer

Step 1: Acceleration of the vehicle
The vehicle moves in a circular horizontal track with
Speed: $v = 10 \, 	ext{m/s}$
Radius: $R = 20 \, 	ext{m}$
Centripetal acceleration of the vehicle (and therefore of the bob inside it):
$ a_c = \frac{v^2}{R} = \frac{10^2}{20} = \frac{100}{20} = 5 \, 	ext{m/s}^2 $
Step 2: Forces on the bob
Weight: $mg$ downward.
String tension has vertical and horizontal components:
Vertical component balances gravity
Horizontal component provides centripetal acceleration (in the non-inertial frame of the vehicle, this is due to pseudo force).
So, if the string makes angle $	heta$ with the vertical, then
$ 	an	heta = \frac{	ext{horizontal acceleration}}{	ext{vertical acceleration}} = \frac{a_c}{g} $
Step 3: Substitute values
$ 	an	heta = \frac{5}{10} = 0.5 $
$ 	heta = 	an^{-1}(0.5) $
Final Answer:
$ \boxed{	an^{-1}(0.5)} \quad 	ext{(Option A)} $

Answer

$	an ^{-1}(0.5)$

Answer

$	an ^{-1}(0.6)$

Answer

$	an ^{-1}(0.7)$

Answer

$	an ^{-1}(0.8)$

Work, Energy and Power & Circular Motion

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