Moment of a force and torque — practice questions

Question 1 · difficulty L2 · understanding

The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters. If a force of $\vec{F} = \hat{i} - \hat{j} + \hat{k}$ acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is __________.

Question 2 · difficulty L2 · understanding

A string is wrapped around the rim of a wheel of moment of inertia $$0.40 \mathrm{~kgm}^2$$ and radius $$10 \mathrm{~cm}$$. The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of $$40 \mathrm{~N}$$. The angular velocity of the wheel after $$10 \mathrm{~s}$$ is $$x \mathrm{~rad} / \mathrm{s}$$, where $$x$$ is __________.

Question 3 · difficulty L2 · understanding

A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52.5 N. The angular acceleration of the cylinder will be _________ rad s$$^{-2}$$.

Question 4 · difficulty L2 · understanding

A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g are put one on the top of the other at the 10.0 cm mark the scale is found to be balanced at 40.0 cm mark. The mass of the metre scale is found to be x $$\times$$ 10 $$-$$2 kg. The value of x is ___________.

Question 5 · difficulty L2 · understanding

A force $$\overrightarrow F$$ = $${4\widehat i + 3\widehat j + 4\widehat k}$$ is applied on an intersection point of x = 2 plane and x-axis. The magnitude of torque of this force about a point (2, 3, 4) is ___________. (Round off to the Nearest Integer)

Question 6 · difficulty L2 · understanding

Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure. A vertical force $$\overrightarrow P$$ of magnitude 100 N is applied at point A of the frame. Suppose the force is $$\overrightarrow P$$ resolved parallel to the arms AB and AC of the frame. The magnitude of the resolved component along the arm AC is xN. The value of x, to the nearest integer, is ___________. [Given : sin(35$$^\circ$$) = 0.573, cos(35$$^\circ$$) = 0.819 sin(110$$^\circ$$) = 0.939, cos(110$$^\circ$$) = $$-$$ 0.342 J

Question 7 · difficulty L2 · understanding

Which of the following are correct expression for torque acting on a body? A. $\vec{\tau}=\vec{r} \times \vec{L}$ B. $\vec{\tau}=\frac{d}{d t}(\vec{r} \times \vec{p})$ C. $\vec{\tau}=\vec{r} \times \frac{d \vec{p}}{d t}$ D. $\vec{\tau}=I \vec{\alpha}$ E. $\vec{\tau}=\vec{r} \times \vec{F}$ ( $\vec{r}=$ position vector; $\vec{p}=$ linear momentum; $\vec{L}=$ angular momentum; $\vec{\alpha}=$ angular acceleration; $I=$ moment of inertia; $\vec{F}=$ force; $t=$ time) Choose the correct answer from the options given below:

• A. A, B, D and E Only
• B. C and D Only
• C. B, C, D and E Only
• D. B, D and E Only

Question 8 · difficulty L2 · understanding

A square Lamina OABC of length 10 cm is pivoted at ' $\mathrm{O}^{\prime}$. Forces act at Lamina as shown in figure. If Lamina remains stationary, then the magnitude of F is :

• A. 10 N
• B. 0 (zero)
• C. 10$\sqrt2$ N
• D. 20 N

Question 9 · difficulty L2 · understanding

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is

• A. 290 g
• B. 200 g
• C. 190 g
• D. 300 g

Question 10 · difficulty L2 · understanding

The torque due to the force $(2 \hat{i}+\hat{j}+2 \hat{k})$ about the origin, acting on a particle whose position vector is $(\hat{i}+\hat{j}+\hat{k})$, would be

• A. $\hat{j}+\hat{k}$
• B. $\hat{i}-\hat{k}$
• C. $\hat{i}-\hat{j}+\hat{k}$
• D. $\hat{i}+\hat{k}$