In the figure shown rod AB is light and rigid while uniform rod CD has mass but is also rigid and hinged at midpoint O. Rod CD can rotate in the plane of diagram without friction about O. The time period of small oscillation of rod CD is T=2πmnk , where m is mass of rod CD and k is spring constant of each spring. Ignoring gravity, find the value of n ? (Assume the rod AB only translates)
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 5.
(Unlock A.I Detailed Solution for FREE)
Best Courses for You
JEE
NEET
Foundation JEE
Foundation NEET
CBSE
Detailed Solution
Effective k on Left side =2k3Let say rod is rotated by small angle θ in clockwise direction∴Extension in spring on left=Compression in spring on right=ℓ2θRestoring torque =FLrL+FRrR=(2k3ℓ2θ+kℓ2θ)(ℓ2)τ=Iα⇒−(2kθ12+kθ4)ℓ2=mℓ212α⇒α=−(5km)θ∴T=2πm5k