A uniform rope of linear mass density $λ$ is placed on a fixed rough $(μ = \frac{3}{4})$ surface of shape of quarter sphere. The upper end of the rope is attached to block of mass $M_{0}$ with the help of ideal spring as shown in figure. The block is released when the spring is in natural length. The maximum energy (in J) stored in the spring if the rope does not slip on the surface is _________.
[Take $λ = 1 k g / m, R = 1 m, g = 10 m / s^{2}, K = 25 N m^{- 1}$ ]

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

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

Taking torque balance about O at just slipping

$τ_{f} = \int_{37}^{90} μ (d m) g \sin θ R = \frac{4}{5} μ g λ R^{2} τ_{m g} = \int_{37}^{90} (d m) g \cos θ R = \frac{2}{5} λ g R^{2} τ_{S P} = K x \times R K x R = \frac{4}{5} λ g R^{2} + \frac{2}{5} λ g R^{2} u = \frac{1}{2} K x^{2} = 2 J$

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th