Work done by a constant and by a variable force — practice questions

Question 1 · difficulty L2 · understanding

A body of mass 1 kg moves along a straight line with a velocity $v=2 x^2$. The work done by the body during displacement from $x=0$ to 5 m is $\_\_\_\_$ J.

• A. 0
• B. 250
• C. 1250
• D. 1000

Question 2 · difficulty L2 · understanding

The rain drop of mass 1 g , starts with zero velocity from a height of 1 km . It hits the ground with a speed of $5 \mathrm{~m} / \mathrm{s}$. The work done by the unknown resistive force is $\_\_\_\_$ J. (take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

• A. -8.75
• B. -8.35
• C. -9.55
• D. -9.98

Question 3 · difficulty L2 · understanding

Given below are two statements : Statement I : An object moves from position $r_1$ to position $r_2$ under a conservative force field $\vec{F}$. The work done by the force is $W=-\int\limits_{r_1}^{r_2} \vec{F} \cdot \overrightarrow{d r}$. Statement II : Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force. In the light of the above statements, choose the correct answer from the options given below :

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

Question 4 · difficulty L2 · understanding

A body of mass 2 kg is moving along x -direction such that its displacement as function of time is given by $x(t) = \alpha t^2 + \beta t + \gamma$ m, where $\alpha = 1 \; m/s^2$, $\beta = 1 \; m/s$ and $\gamma = 1 \; m$. The work done on the body during the time interval $t = 2 \; s$ to $t = 3 \; s$, is ________ J.

• A. 42
• B. 24
• C. 49
• D. 12

Question 5 · difficulty L2 · understanding

A force $\mathrm{F}=\alpha+\beta \mathrm{x}^2$ acts on an object in the x -direction. The work done by the force is 5 J when the object is displaced by 1 m . If the constant $\alpha=1 \mathrm{~N}$ then $\beta$ will be

• A. $15 \mathrm{~N} / \mathrm{m}^2$
• B. $10 \mathrm{~N} / \mathrm{m}^2$
• C. $12 \mathrm{~N} / \mathrm{m}^2$
• D. $8 \mathrm{~N} / \mathrm{m}^2$

Question 6 · difficulty L2 · understanding

A force $\overrightarrow{\mathrm{F}}=2 \hat{i}+\mathrm{b} \hat{j}+\hat{k}$ is applied on a particle and it undergoes a displacement $\hat{i}-2 \hat{j}-\hat{k}$ What will be the value of $b$, if work done on the particle is zero.

• A. $\frac{1}{3}$
• B. $\frac{1}{2}$
• C. 0
• D. 2

Question 7 · difficulty L2 · understanding

A particle of mass $$m$$ moves on a straight line with its velocity increasing with distance according to the equation $$v=\alpha \sqrt{x}$$, where $$\alpha$$ is a constant. The total work done by all the forces applied on the particle during its displacement from $$x=0$$ to $$x=\mathrm{d}$$, will be :

• A. $$\frac{\mathrm{m}}{2 \alpha^2 \mathrm{~d}}$$
• B. $$\frac{\mathrm{md}}{2 \alpha^2}$$
• C. $$\frac{\mathrm{m} \alpha^2 \mathrm{~d}}{2}$$
• D. $$2 \mathrm{~m} \alpha^2 \mathrm{~d}$$

Question 8 · difficulty L2 · understanding

A body of mass $$50 \mathrm{~kg}$$ is lifted to a height of $$20 \mathrm{~m}$$ from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be :

• A. $$2: 1$$
• B. $$\sqrt{3}: 2$$
• C. $$1: 1$$
• D. $$1: 2$$

Question 9 · difficulty L2 · understanding

A block of mass $$100 \mathrm{~kg}$$ slides over a distance of $$10 \mathrm{~m}$$ on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4, then the work done against friction $$(\operatorname{in} J$$) is :

• A. 3900
• B. 4500
• C. 4200
• D. 4000

Question 10 · difficulty L2 · understanding

A body of mass 'm' dropped from a height 'h' reaches the ground with a speed of 0.8$$\sqrt {gh}$$. The value of workdone by the air-friction is :

• A. $$-$$0.68 mgh
• B. mgh
• C. 1.64 mgh
• D. 0.64 mgh