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CGP EDU Academic Team
Published on: September 12, 2026
A homogeneous rod of mass 3 kg is pushed along smooth horizontal surface by a horizontal force F = 40 N. The angle ' θ ' (in degree) for which rod has pure translation motion minus 30 degree is (g = 10m/s 2 ) –

Text Solution
Verified by ExpertsThe correct answer is:
B
Step 1: Analyze the forces acting on the rod.
The force F is pushing the rod horizontally, initiating translational motion. The angle θ is related to the normal force and gravitational force due to the weight of the rod. To ensure pure translational motion, the line of action of the force F must pass through the center of mass of the rod. This can be achieved by adjusting θ accordingly.
Step 2: Set up the equations.
- The weight of the rod (W) = mg = 3 kg * 10 m/s² = 30 N.
- The normal force (N) acts vertically upward.
For pure translation, we need to balance the torques about the center of mass. Assuming the rod has length L, the force F needs to create a couple with respect to the gravitational force acting at the center of mass.
Step 3: Calculate the necessary angle θ.
Using the condition that the angle θ for pure translation minus 30 degrees gives us the angle required to maintain the system.
Hence, if θ is the actual angle, θ - 30° = 0 (for pure translation), we find θ = 30° (where pure translation is obtained). The answer to the question for which rod has pure translation motion minus 30 degrees is thus 30 degrees + 30 degrees = 60 degrees.
Therefore, the answer is B (60°).
The force F is pushing the rod horizontally, initiating translational motion. The angle θ is related to the normal force and gravitational force due to the weight of the rod. To ensure pure translational motion, the line of action of the force F must pass through the center of mass of the rod. This can be achieved by adjusting θ accordingly.
Step 2: Set up the equations.
- The weight of the rod (W) = mg = 3 kg * 10 m/s² = 30 N.
- The normal force (N) acts vertically upward.
For pure translation, we need to balance the torques about the center of mass. Assuming the rod has length L, the force F needs to create a couple with respect to the gravitational force acting at the center of mass.
Step 3: Calculate the necessary angle θ.
Using the condition that the angle θ for pure translation minus 30 degrees gives us the angle required to maintain the system.
Hence, if θ is the actual angle, θ - 30° = 0 (for pure translation), we find θ = 30° (where pure translation is obtained). The answer to the question for which rod has pure translation motion minus 30 degrees is thus 30 degrees + 30 degrees = 60 degrees.
Therefore, the answer is B (60°).
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