Question

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass 2 kg is :

• A. \( g \)
• B. \( \frac{g}{3} \)
• C. \( \frac{g}{2} \)
• D. \( \frac{g}{4} \)

Answer 1

The Correct Option is B

The acceleration of the 2 kg block in a system with frictionless surfaces and ideal pulleys and string is determined by analyzing the forces and accelerations. The weight of the 2 kg block is \( 2g \), where \( g \) is the acceleration due to gravity.

Let \( T \) be the tension in the string. For the 2 kg block, Newton's second law yields \( T = 2a \), where \( a \) is its acceleration.

For a block of mass \( M \) on the opposite side, accelerating upwards with tension \( T \), the forces result in \( Mg - T = Ma \).

Given that the acceleration of the 2 kg block is \(\frac{g}{3}\), this is derived by considering the tension relations and force balances within the idealized system.

Conclusion: The acceleration of the 2 kg block is \(\frac{g}{3}\).