Performs SHM if!

Classical Mechanics Level 5

A rod of mass m m and length l l hinged about the lowest point is attached to spring of spring constant ( k k ) at the top most point as shown in figure (Gravity is vertically downward). The rod will perform angular SHM about shown mean position with small amplitude if :-

( A ) k > m g 2 l (A) k> \frac{mg}{2l}

( B ) k > m g 4 l (B) k> \frac{mg}{4l}

( C ) k > m g 3 l (C) k> \frac{mg}{3l}

( D ) k > m g l (D) k> \frac{mg}{l}

C C A , B , C , D A,B,C,D A , C , D A,C,D A , D A,D B , C , D B,C,D B B None of These B , D B,D

Nishant Rai by Nishant Rai , 25, India

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1 solution

Nishant Rai
May 31, 2015

If the rod is displaced an angle θ \theta , (considering θ \theta to be very small)

→ ( k l θ ) l > m g l 2 sin ⁡ θ \rightarrow (kl \theta)l > \frac{mgl}{2} \sin \theta

→ k l 2 θ > m g l 2 θ \rightarrow kl^2 \theta > \frac{mgl}{2} \theta

→ k > m g 2 l \rightarrow k > \frac{mg}{2l}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

@Tanishq Varshney @Guru Prasaadh i have corrected the problem. Now try! Sorry for the inconvenience.

Nishant Rai - 6 years ago

yeah same solution...nice problem for jee ...upvoted.

rajdeep brahma - 3 years, 4 months ago

If k>mg/2l then it is not necessary that it is also greater than mg/l For example suppose mg/l =1 then ans is k>0.5 but this does not imply that k>1 k can be 0.75 or any other value between 0.5 and 1

Kumar Krish - 2 years, 4 months ago

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