Two bodies of mass 4 kg and 6 kg tied to the ends of a massless string. The string passes over a pulley which is frictionless. The acceleration of the system in terms of acceleration due to gravity (g) is:

• A) g
• B) g/2
• C) g/5
• D) g/10

To find the acceleration of the system with two masses tied to a string over a frictionless pulley, we can use Newton's second law. Let's denote the masses as m1 = 4 kg and m2 = 6 kg. The force acting on the system is due to the difference in weight of the two masses.

Calculating the Forces

The gravitational force acting on each mass can be calculated as:

• Weight of m1: W1 = m1 * g = 4g
• Weight of m2: W2 = m2 * g = 6g

Net Force and Acceleration

The net force (F_net) acting on the system is the difference in weights:

F_net = W2 - W1 = 6g - 4g = 2g

The total mass of the system (m_total) is the sum of both masses:

m_total = m1 + m2 = 4 kg + 6 kg = 10 kg

Using Newton's Second Law

According to Newton's second law, F = m * a, we can express the acceleration (a) as:

a = F_net / m_total = (2g) / (10 kg) = g / 5

Final Answer

Thus, the acceleration of the system in terms of acceleration due to gravity (g) is:

g/5