Question

Reason
The velocity of oscillating bob in simple harmonic motion is maximum at the mean position.
Assertion
For an oscillating simple pendulum the tension in the string is maximum at the mean position and minimum at the extreme position.
For an oscillating simple pendulum the tension in the string is maximum at the mean position and minimum at the extreme position.

Answer 1

Correct option is B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
In simple pendulum, when bob is in deflection position, the tension in the string is $$T=mg\cos\theta+\dfrac{mv^{2}}{l}$$. Since the value of $$\theta$$ is different at different positions, hence tension in the string is not constant throughout the oscillation. At end points $$\theta$$ is maximum; the value of $$\cos\theta$$ is least, hence the value of tension in the string is least. At the mean position,the value of $$\theta=0^{o}$$ and $$\cos 0^{o}=1$$, so the value of tension is largest. Also velocity is given by $$v=\omega \sqrt{a^{2}-y^{2}}$$ which is maximum when $$y = 0$$, at mean position.