A large plank of mass ‘3M’ is kept on a frictionless horizontal surface, one end of plank is connected with a spring of force constant k = 110 N/m as shown in the figure. A cylinder of mass ‘2M’ and radius ‘R’ is placed on the upper surface of plank. Friction force is sufficient to prevent slipping between cylinder and plank. Now plank is slightly displaced from its equilibrium position, then its angular frequency of oscillation is given by $\sqrt{N} r a d / s$ . Find the value of N. (Given M = 1kg)

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

answer is 30.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Let ‘x’ is the displacement of plank from its equilibrium position
$f + k x = (3 M) a p .... (i) f . R = \frac{(2 M) R^{2}}{2} α ... (i i) a_{c} = \frac{f}{2 M} .... (i i i) a_{c} + R α = - a p .... (i v)$
On solving $ω = \sqrt{\frac{3 k}{11 M}} = \sqrt{30} r a d / s$
Question Image