question_answer

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

A)             If both assertion and reason are true and the reason is the correct explanation of the assertion.

B)             If both assertion and reason are true but reason is not the correct explanation of the assertion.

C)             If assertion is true but reason is false.

D)             If the assertion and reason both are false.

E)             If assertion is false but reason is true.

Correct Answer: B

Solution :

                   In simple pendulum, when bob is in deflection position, the tension in the string is \[T=mg\cos \theta +\frac{m{{v}^{2}}}{l}.\] Since the value of q is different at different positions, hence tension in the string is not constant throughout the oscillation. At end points q 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 \[\theta =0{}^\circ \] and \[\cos 0{}^\circ =1,\] 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.