Question

If the string connecting \( m \) and the ground is cut, find the speed with which the \( 2m \) block hits the ground as shown. \( g = 10 \, \text{m/s}^2 \)

• A. 3 m/s
• B. 4 m/s
• C. \( 2\sqrt{6} \) m/s
• D. \( 6\sqrt{2} \) m/s

Hint:

Conservation of energy helps in solving problems involving free fall and collision where potential energy is converted into kinetic energy.

Answer 1

The Correct Option is C

Step 1: Apply conservation of energy.
In this system, the potential energy of the block of mass \( m \) is converted into the kinetic energy of both blocks after the string is cut. Step 2: Set up the energy equation.
The initial potential energy is \( m g h \), where \( h = 3.6 \, \text{m} \) is the height. The final kinetic energy is the sum of the kinetic energies of both blocks: \[ \frac{1}{2} (m) v^2 + \frac{1}{2} (2m) v_2^2. \] Using the relation that both blocks move together for the instant after the string is cut, we find the speed of the \( 2m \) block just before it hits the ground is \( 2\sqrt{6} \) m/s. Final Answer: \[ \boxed{2\sqrt{6} \, \text{m/s}}. \]