Question

In the arrangement shown in the Figure pulley is smooth and massless and string is light. Friction coefficient between A and B is µ. Friction is absent between A and plane. Select the correct alternative(s)

(A) acceleration of the system is zero if \(\mu \ge \frac{m_B - m_A}{2m_B}\) tan\(\theta\) and m_B > m_A

(B) Force of friction between A and B is zero if m_A = m_B

(C) B moves upwards if m_B < m_A

(D) Tension in the string is mg (sin θ−µ cosθ) if m_A = m_B = m_C

Answer 1

Correct options are (A) and (B)

Tension itself balances both the masses.

So, no necessity for any friction.

C: we cannot explicitly say that.

We need more information on µ.

D: when m_A = m_B;

Put friction f = 0 in (i) and (iii)

And subtract them to get Tension ‘T’.

Answer 2

Correct answer is 

(A) acceleration of the system is zero if \(\mu \ge \frac{m_B - m_A}{2m_B}\) tan\(\theta\) and m_B > m_A

(B) Force of friction between A and B is zero if m_A = m_B