Equilibrium of concurrent forces — NEET & JEE Questions

Question 1 · difficulty L1 · recall

For a particle to be in equilibrium under concurrent forces, the vector sum of all forces must be

• A. zero
• B. equal to its mass
• C. maximum
• D. parallel to its velocity

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 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 4 · 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 5 · 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 6 · 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 7 · difficulty L2 · understanding

Statement : 1 If three forces $${\overrightarrow F _1},{\overrightarrow F _2}$$ and $${\overrightarrow F _3}$$ are represented by three sides of a triangle and $${\overrightarrow F _1} + {\overrightarrow F _2} = - {\overrightarrow F _3}$$, then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement : 2 A triangle made up of three forces $${\overrightarrow F _1}$$, $${\overrightarrow F _2}$$ and $${\overrightarrow F _3}$$ as its sides taken in the same order, satisfy the condition for translatory equilibrium. In the light of the above statements, choose the most appropriate answer from the options given below :

• A. Statement - I is false but Statement - II is true
• B. Statement - I is true but Statement - II is false
• C. Both Statement-I and Statement-II are false
• D. Both Statement-I and Statement-II are true

Question 8 · difficulty L3 · understanding

Two forces $$\overline{\mathrm{F}}_1$$ and $$\overline{\mathrm{F}}_2$$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $$\vec{F}_1$$ and $$\vec{F}_2$$ is $$\cos ^{-1}\left(\frac{1}{n}\right)$$. The value of $$|n|$$ is _______.

Question 9 · difficulty L3 · understanding

A mass of 10 kg is suspended vertically by a rope of length 5 m from the roof. A force of 30 N is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is $$\theta$$ = tan $$-$$1 (x $$\times$$ 10 $$-$$1 ). The value of x is ____________. (Given, g = 10 m/s 2 )

Question 10 · difficulty L3 · understanding

A flexible chain of mass $m$ hangs between two fixed points at the same level. The inclination of the chain with the horizontal at the two points of support is $30^{\circ}$. Considering the equilibrium of each half of the chain, the tension of the chain at the lowest point is $\_\_\_\_$ .

• A. $m \mathrm{~g}$
• B. $\frac{\sqrt{3}}{2} m g$
• C. $\frac{1}{2} m g$
• D. $\sqrt{3} m \mathrm{~g}$