Equilibrium of rigid bodies Quiz

1. A uniform rod of weight $50$ N is hinged at one end and held by a horizontal force $P$ at the other end, at $\tan\theta=\frac34$ to the vertical. Find $P$.

• A. $18.75$ N
• B. $37.5$ N
• C. $33.3$ N
• D. $66.7$ N

2. A uniform ladder of weight $W$ rests against a smooth wall at $\alpha=45^\circ$ to the horizontal. What is the least coefficient of friction at the ground?

• A. $1$
• B. $0.25$
• C. $2$
• D. $0.5$

3. A uniform solid cuboid with square base of side $0.4$ m and height $1.2$ m stands on an incline. At what $\tan\theta$ does it topple?

• A. $\frac15$
• B. $\frac13$
• C. $\frac23$
• D. $3$

4. A block topples at $\tan\theta=0.8$. For which value of $\mu$ does it slide before toppling?

• A. $0.9$
• B. $1.2$
• C. $0.7$
• D. $0.8$ exactly

5. A body hangs freely from a point $P$. Which statement is correct?

• A. The centre of mass is level with $P$
• B. The centre of mass is vertically below $P$
• C. The centre of mass is on the surface
• D. The centre of mass is vertically above $P$