Advertisements
Advertisements
प्रश्न
Calculate the total torque acting on the body shown in the following figure about the point O.
Advertisements
उत्तर
Torque about a point = Total force × Perpendicular distance
Let the anticlockwise torque and clockwise acting torque be positive and negative, respectively.
Torque at O due to 5 N force is zero as it is passing through O.
Torque at O due to 15 N force,
\[\tau_1 = 15 \times 6 \times {10}^{- 2} \times \sin37^\circ\]
\[ = 15 \times 6 \times {10}^{- 2} \times \frac{3}{5}\]
\[ = 0 . 54 N - m .........\left(\text{anticlockwise} \right)\]
Torque at O due to 10 N force,
\[\tau_2 = 10 \times 4 \times {10}^{- 2} = 0 . 4 N - m ........\left(\text{clockwise} \right)\]
Torque at O due to 20 N force,
\[\tau_3 = 20 \times 4 \times {10}^{- 2} \times \sin30^\circ\]
\[ = 20 \times 4 \times {10}^{- 2} \times \frac{1}{2}\]
\[ = 0 . 4 N - m .........\left(\text{Anticlockwise} \right)\]
Resultant torque acting at O,
\[\tau = \left( 0 . 54 - 0 . 4 + 0 . 4 \right)\]
\[ = 0 . 54 N - m \left(\text{Anticlockwise} \right)\]
APPEARS IN
संबंधित प्रश्न
Explain why friction is necessary to make the disc in Figure roll in the direction indicated
(a) Give the direction of frictional force at B, and the sense of frictional torque, before perfect rolling begins.
(b) What is the force of friction after perfect rolling begins?
The torque of the weight of any body about any vertical axis is zero. If it always correct?
If several forces act on a particle, the total torque on the particle may be obtained by first finding the resultant force and then taking torque of this resultant. Prove this. Is this result valid for the forces acting on different particles of a body in such a way that their lines of action intersect at a common point?
A body is in translational equilibrium under the action of coplanar forces. If the torque of these forces is zero about a point, is it necessary that it will also be zero about any other point?
A ladder is resting with one end on a vertical wall and the other end on a horizontal floor. If it more likely to slip when a man stands near the bottom or near the top?
Equal torques act on the disc A and B of the previous problem, initially both being at rest. At a later instant, the linear speeds of a point on the rim of A and another point on the rim of B are \[\nu_A\] and \[\nu_B\] respectively. We have
The density of a rod gradually decreases from one end to the other. It is pivoted at an end so that it can move about a vertical axis though the pivot. A horizontal force F is applied on the free end in a direction perpendicular to the rod. The quantities, that do not depend on which end of the rod is pivoted, are ________________ .
A simple pendulum of length l is pulled aside to make an angle θ with the vertical. Find the magnitude of the torque of the weight ω of the bob about the point of suspension. When is the torque zero?
A flywheel of moment of inertia 5⋅0 kg-m2 is rotated at a speed of 60 rad/s. Because of the friction at the axle it comes to rest in 5⋅0 minutes. Find (a) the average torque of the friction (b) the total work done by the friction and (c) the angular momentum of the wheel 1 minute before it stops rotating.
Two discs of the same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of the disc with angular velocities ω1 and ω2. They are brought in to contact face to face coinciding with the axis of rotation. The expression for loss of energy during this process is, ______
The ratio of the acceleration for a solid sphere (mass m and radius R) rolling down an incline of angle θ without slipping and slipping down the incline without rolling is, ______
A particle of mass m is moving in yz-plane with a uniform velocity v with its trajectory running parallel to + ve y-axis and intersecting z-axis at z = a (Figure). The change in its angular momentum about the origin as it bounces elastically from a wall at y = constant is ______.
Figure shows two identical particles 1 and 2, each of mass m, moving in opposite directions with same speed v along parallel lines. At a particular instant, r1 and r2 are their respective position vectors drawn from point A which is in the plane of the parallel lines. Choose the correct options:
- Angular momentum l1 of particle 1 about A is l1 = mvd1
- Angular momentum l2 of particle 2 about A is l2 = mvr2
- Total angular momentum of the system about A is l = mv(r1 + r2)
- Total angular momentum of the system about A is l = mv (d2 − d1)
⊗ represents a unit vector coming out of the page.
⊗ represents a unit vector going into the page.
A uniform sphere of mass m and radius R is placed on a rough horizontal surface (Figure). The sphere is struck horizontally at a height h from the floor. Match the following:
| Column I | Column II | |
| (a) h = R/2 | (i) | Sphere rolls without slipping with a constant velocity and no loss of energy. |
| (b) h = R | (ii) | Sphere spins clockwise, loses energy by friction. |
| (c) h = 3R/2 | (iii) | Sphere spins anti-clockwise, loses energy by friction. |
| (d) h = 7R/5 | (iv) | Sphere has only a translational motion, looses energy by friction. |
A spherical shell of 1 kg mass and radius R is rolling with angular speed ω on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is `a/3 R^2` ω. The value of a will be:
Angular momentum of a single particle moving with constant speed along the circular path ______.
A solid sphere is rotating in free space. If the radius of the sphere is increased while keeping the mass the same, which one of the following will not be affected?
