Physics · Equilibrium of rigid bodies, rigid body rotation and equations of rotational motion, comparison of linear and rotational motions
In a physical balance working on the principle of moments, when weight is placed
In a physical balance working on the principle of moments, when \( 5 \mathrm{mg} \) weight is placed on the left plan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?
- A. Both the arms are of same length.
- B. Every object that is weighed using this balance appears lighter than its actual weight
- C. Left arm is longer than the right arm.
- D. Left arm is shorter than the right arm.
Step-by-step solution
Let the masses of empty pans be m. Let left arm length L_l and right arm length L_r. Initially, without the 5 mg weight, the beam is not horizontal, meaning torques are unequal: m g L_l ≠ m g L_r. When 5 mg is added to left pan, beam becomes horizontal, so net torque zero: (m+5) g L_l = m g L_r. Since m+5 > m, L_l must be less than L_r for equality. Hence left arm is shorter than right arm.
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