Question

A ring of mass 200 gram is attached to one end of a light spring of force constant 100 N/m and natural length 10 cm. The ring is constrained to move on a rough wire in the shape of quarter ellipse of major axis 24 cm and minor axis 16 cm with its centre at origin. The plane of ellipse is vertical and wire is fixed at points A and B as shown in figure. Initially ring is at A with other end of spring fixed at origin. Ring is given a horizontal velocity of 10 m/s towards right so that it just reaches point B, then select the correct alternative (s) (g = 10 m/s²)

s

• A. Work done by friction is – 10 Joule
• B. At B energy stored in spring is more than energy stored at A.
• C. Work done by friction is –10.16 Joule
• D. Work done by spring force is positive

Answer 1

Answer: (C)

Work done by friction is –10.16 Joule

Answer 2

Apply work energy theorem

Wg + W_N + W_fr + W_s = DK

W_fr = $- \frac { 1 } { 2 } m v ^ { 2 } - \operatorname { mg } ( 0.08 )$

W_fr = – 10.16