Circular MotionHard
Question
A simple pendulum of length L and mass (bob) M is oscillating in a plane about vertical line between angular limits - φ and + φ. For an angular displacement θ (|θ| < φ), the tension in the string and the velocity of the bob are T and v respectively. The following relations holds good under the above conditions
Options
A.T cos θ = Mg
B.T - Mg cos θ = 
C.the magnitude of the tangential acceleration of the bob |aT| = g sin θ
D.T = Mg cos θ
Solution
Motion of pendulum is part of a circular motion. In circular motion it is better to resolve the forces in two perpendicular directions. First along radius (towards centre) and second along tangential. Along radius net force should be
equal to
and along tangent it should equal to maT, where aT is the tangential acceleration in the figure. T - Mg cos θ =
and Mg cos θ = M aT or aT = g cos θ
∴ Correct options are (b) and (c).
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