A cart consists of a body of mass m and two wheels, each of mass m and radius R. The cart is attached to a spring of constant k. The other end of the spring is fixed to a wall as shown in the figure. Friction between wheels and ground is sufficient to prevent slipping, If time period of oscillation is $β \times 2 π \sqrt{\frac{m}{k}}$ then find the value of $β$

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

answer is 2.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

From energy conservation

$\frac{1}{2} k x^{2} + 2 (\frac{1}{2} I ω^{2} + \frac{1}{2} m v^{2}) + \frac{1}{2} m v^{2} = 0 (I = \frac{m R^{2}}{2}) \Rightarrow k x^{2} + 4 m v^{2} = 0 \Rightarrow 2 k x . \frac{d x}{d t} + (4 m) 2 v \frac{d v}{d t} = 0 \Rightarrow a = - (\frac{k}{4 m}) x \Rightarrow ω = \sqrt{\frac{k}{4 m}}$