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Torque - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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Torque is considered one of the most asked concept.
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39 Questions around this concept.
Solve by difficulty
A force of $-F \hat{k}$ acts on O , the origin of the coordinate system. The torque about the point $(1,-1)$ is :
The torque of a force about the origin is
. If the force acts on a particle whose position vector is
, then the value of
will be
A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is :
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A slender uniform rod of mass M and length l is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod, when it makes an angle θ with the vertical, is :
A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2, the number of rotations made by the pulley before its direction of motion is reversed, is
Match List I with List II:
Choose the correct answer from the options given below:
Constant torque acting on a uniform circular wheel changes its angular momentum from A to 4A in 4 seconds. The magnitude of this torque is
Figure 7.5 shows a lamina in the $x$-y plane. Two axes $z$ and $z$ ' pass perpendicular to its plane. A force $F$ acts in the plane of the lamina at point $P$ as shown. Which of the following is true? (The point $P$ is closer to the $z^{\prime}$-axis than the $z$-axis.)
(a) Torque $\tau$ caused by F about the z -axis is along $-\hat{k}$
(b) Torque $\tau^{\prime}$ caused by F about $\mathrm{z}^{\prime}$ axis is along $-\hat{k}$
(c) Torque $\tau$ caused by F about the z-axis is greater in magnitude than that about the z-axis.
(d) Total torque is given by $\tau=\tau+\tau^{\prime}$
The torque due to the force $(2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+2 \hat{\mathrm{k}})$ about the origin, acting on a particle whose position vector is $(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})$, would be
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Torque
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Vector product of Force vector and position vector is known as torque.
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- $\vec{\tau}=\vec{r} \times {\vec{F}}$
- Its direction is always perpendicular to the plane containing vector r and F and with the help of right hand screw rule we can find it.
- The magnitude of torque is calculated by using either
- $\tau=r_1 F$ or $\tau=r \cdot F_1$
$r_1=$ perpendicular distance from origin to the line of force.
$F_1=$ component of force perpendicular to line joining force.
- $\tau=r . F \cdot \sin \phi$Where $\phi {\text { is the angle between vector } r \text { and } \mathrm{F}}$
- $\tau_{\text {max }}=r . F\left(\right.$ when $\left.\phi=90^{\circ}\right)$
- $\tau_{\min }=0\left(\right.$ when $\left.\phi=0^0\right)$
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If a pivoted, hinged body tends to rotate due to an applied force, then it is said that torque is acted on body by force.
Example-
In the rotation of a hinged door when we apply torque with the help of force F.
- SI Unit- Newton-metre
- Dimension- $M L^2 T^{-2}$
- If a body is acted upon by more than one force, then we get the resultant torque by doing vector sum of each torque.
$
\tau=\tau_1+\tau_2+\tau_3 \ldots \ldots
$
- Just like force is the cause of translatory motion similarly Torque is the cause of rotatory motion.
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