Question

A pendulum consisting of a small heavy bob suspended from a rigid rod oscillates in a vertical plane (Fig.). When the bob passes through the position of equilibrium the rod is subjected to a tension equal to twice the weight of the bob. Through what maximum angle a from the vertical will the pendulum be deflected? Disregard the weight of rod and resistance of the air.

• A. 30⁰
• B. 45⁰
• C. 60⁰
• D. 75⁰

Answer 1

Answer: (C)

60⁰

Answer 2

See Newton's second law to find the velocity when the bob passes through the position of equilibrium

v² = $\frac { ( \mathrm { F } - \mathrm { mg } ) \ell } { \mathrm { m } }$ = gl

From the equation of the law of conservation of energy, $\frac { \mathrm { mv } ^ { 2 } } { 2 }$ = mgh, it is possible to find the height from which the bob dropped

h = $\frac { v ^ { 2 } } { 2 g }$ = $\frac { \ell } { 2 }$ .

cos a = h/l = ½