Identify correct statement among the following

Difficult

A

The greater the mass of a pendulum bob, the shorter is its frequency of oscillation
B

A simple pendulum with a bob of mass M swings with an angular amplitude of $40^{o}$ . When its angular amplitude is $20^{o}$ , the tension in the string is less than $Mgcos 20^{o}$ .
C

As the length of a simple pendulum is increased, the maximum velocity of its bob during its oscillation will also decreases
D

The fractional change in the time period of a pendulum on changing the temperature is independent of the length of the pendulum

Solution

$T \cos θ = m g T = \frac{m g}{\cos 20} > m g \cos 20 °$
timeperiod
$T = 2 π \sqrt{\frac{l}{g}} If l increases T increases ω (= \frac{2 π}{T}) decreases, velocity (v = rω) decreases$

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