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JEE Advanced2008PhysicsOscillationsActual

Paragraph: A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L

Options

  1. Ag M k
  2. Bg M 2 k
  3. Cg 3 M k
  4. Dg 5 M 2 k

Correct answer

C. g 3 M k

Step-by-step solution

In case of pure rolling, mechanical energy will remain conserved. array rlrl & & 1 2 M v₀^2+ 1 2 ( 1 2 M R^2 ) ( v₀ R )^2 & =2 [ 1 2 k x_ ^2 ] & & x_ & = 3 M 4 k v₀ & As & & = 2 k x 3 & f_ & = M g= 2 k x_ 3 = 2 k 3 3 M 4 k v₀ & v₀ & = g 3 M k array correct option is (c).

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