Equilibrium of concurrent forces — practice questions

Question 1 · difficulty L2 · understanding

Four forces are acting at a point $$\mathrm{P}$$ in equilibrium as shown in figure. The ratio of force $$\mathrm{F}_{1}$$ to $$\mathrm{F}_{2}$$ is $$1: x$$ where $$x=$$ _____________.

Question 2 · difficulty L2 · understanding

A body of mass $m$ is suspended by two strings making angles $\theta_1$ and $\theta_2$ with the horizontal ceiling with tensions $T_1$ and $T_2$ simultaneously. $T_1$ and $T_2$ are related by $T_1=\sqrt{3} T_2$, the angles $\theta_1$ and $\theta_2$ are

• A. $\theta_1=30^{\circ} \theta_2=60^{\circ}$ with $T_2=\frac{3 \mathrm{mg}}{4}$
• B. $\theta_1=45^{\circ} \theta_2=45^{\circ}$ with $T_2=\frac{3 m g}{4}$
• C. $\theta_1=30^{\circ} \theta_2=60^{\circ}$ with $T_2=\frac{4 m g}{5}$
• D. $\theta_1=60^{\circ} \theta_2=30^{\circ}$ with $T_2=\frac{m g}{2}$

Question 3 · difficulty L2 · understanding

A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitudes of tensions $\mathrm{T}_1$ and $\mathrm{T}_2$, respectively, are (in N ) : (Take acceleration due to gravity $10 \mathrm{~m} / \mathrm{s}^2$ )

• A. $5 \sqrt{3}, 5$
• B. $5 \sqrt{3}, 5 \sqrt{3}$
• C. 5,5
• D. $5,5 \sqrt{3}$

Question 4 · difficulty L2 · understanding

A $$1 \mathrm{~kg}$$ mass is suspended from the ceiling by a rope of length $$4 \mathrm{~m}$$. A horizontal force '$$F$$' is applied at the mid point of the rope so that the rope makes an angle of $$45^{\circ}$$ with respect to the vertical axis as shown in figure. The magnitude of $$F$$ is : (Assume that the system is in equilibrium and $$g=10 \mathrm{~m} / \mathrm{s}^2$$)

• A. 1 N
• B. 10 N
• C. $$\frac{10}{\sqrt{2}} N$$
• D. $$\frac{1}{10 \times \sqrt{2}} N$$

Question 5 · difficulty L2 · understanding

A heavy iron bar, of weight $$W$$ is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle $$\theta$$ with the horizontal. The weight experienced by the person is :

• A. $$W \sin \theta$$
• B. $$W$$
• C. $$\frac{W}{2}$$
• D. $$W \cos \theta$$

Question 6 · difficulty L2 · understanding

A body of weight $$200 \mathrm{~N}$$ is suspended from a tree branch through a chain of mass $$10 \mathrm{~kg}$$. The branch pulls the chain by a force equal to (if $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$) :

• A. 300 N
• B. 100 N
• C. 150 N
• D. 200 N

Question 7 · difficulty L2 · understanding

Three forces $$F_{1}=10 \mathrm{~N}, F_{2}=8 \mathrm{~N}, \mathrm{~F}_{3}=6 \mathrm{~N}$$ are acting on a particle of mass $$5 \mathrm{~kg}$$. The forces $$\mathrm{F}_{2}$$ and $$\mathrm{F}_{3}$$ are applied perpendicularly so that particle remains at rest. If the force $$F_{1}$$ is removed, then the acceleration of the particle is:

• A. $$4.8 \mathrm{~ms}^{-2}$$
• B. $$7 \mathrm{~ms}^{-2}$$
• C. $$2 \mathrm{~ms}^{-2}$$
• D. $$0.5 \mathrm{~ms}^{-2}$$

Question 8 · difficulty L2 · understanding

As shown in figure, a $$70 \mathrm{~kg}$$ garden roller is pushed with a force of $$\vec{F}=200 \mathrm{~N}$$ at an angle of $$30^{\circ}$$ with horizontal. The normal reaction on the roller is (Given $$\mathrm{g=10~m~s^{-2}}$$)

• A. 800 N
• B. 600 N
• C. 200$$\sqrt3$$ N
• D. 800$$\sqrt2$$ N

Question 9 · difficulty L2 · understanding

A block of $\sqrt{3} \mathrm{~kg}$ is attached to a string whose other end is attached to the wall. An unknown force $\mathrm{F}$ is applied so that the string makes an angle of $30^{\circ}$ with the wall. The tension $\mathrm{T}$ is: (Given $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )

• A. 15 N
• B. 10 N
• C. 25 N
• D. 20 N

Question 10 · difficulty L2 · understanding

For a free body diagram shown in the figure, the four forces are applied in the 'x' and 'y' directions. What additional force must be applied and at what angle with positive x-axis so that the net acceleration of body is zero?

• A. $$\sqrt{2} N, 45^{\circ}$$
• B. $$\sqrt{2} N, 135^{\circ}$$
• C. $$\frac{2}{\sqrt{3}} N, 30^{\circ}$$
• D. $$2 N, 45^{\circ}$$