Advertisements
Advertisements
प्रश्न
A cubical block of mass M and edge a slides down a rough inclined plane of inclination θ with a uniform velocity. The torque of the normal force on the block about its centre has a magnitude
विकल्प
zero
Mga
Mga sinθ
\[\frac{1}{2}\text{Mga }\sin\theta\]
Advertisements
उत्तर
\[\frac{1}{2}\text{Mga }\sin\theta\]
Let N be the normal reaction on the block.
From the free body diagram of the block, it is clear that the forces N and mgcosθ pass through the same line. Therefore, there will be no torque due to N and mgcosθ. The only torque will be produced by mgsinθ.
\[\therefore \overrightarrow{\tau} = \overrightarrow{F} \times \overrightarrow{r}\]
Since a is the edge of the cube, \[r = \frac{a}{2}\]
Thus, we have
\[\tau = mg\sin\theta \times \frac{a}{2}\]
\[= \frac{1}{2}mga\sin\theta\]
APPEARS IN
संबंधित प्रश्न
If the ice at the poles melts and flows towards the equator, how will it affect the duration of day-night?
A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 4r is made from an iron plate of thickness t/4. The relation between the moments of inertia IA and IB is __________ .
A closed cylindrical tube containing some water (not filling the entire tube) lies in a horizontal plane. If the tube is rotated about a perpendicular bisector, the moment of inertia of water about the axis __________ .
A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top on an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. Least time will be taken in reaching the bottom by ___________ .
In the previous question, the smallest kinetic energy at
the bottom of the incline will be achieved by ___________ .
A string of negligible thickness is wrapped several times around a cylinder kept on a rough horizontal surface. A man standing at a distance l from the cylinder holds one end of the string and pulls the cylinder towards him (see the following figure). There is no slipping anywhere. The length of the string passed through the hand of the man while the cylinder reaches his hands is _________ .
Consider a wheel of a bicycle rolling on a level road at a linear speed \[\nu_0\] (see the following figure)
(a) the speed of the particle A is zero
(b) the speed of B, C and D are all equal to \[v_0\]
(c) the speed of C is 2 \[v_0\]
(d) the speed of B is greater than the speed of O.
Three particles, each of mass 200 g, are kept at the corners of an equilateral triangle of side 10 cm. Find the moment of inertial of the system about an axis passing through one of the particles and perpendicular to the plane of the particles.
Find the moment of inertia of a pair of spheres, each having a mass mass m and radius r, kept in contact about the tangent passing through the point of contact.
The moment of inertia of a uniform rod of mass 0⋅50 kg and length 1 m is 0⋅10 kg-m2about a line perpendicular to the rod. Find the distance of this line from the middle point of the rod.
The radius of gyration of a uniform disc about a line perpendicular to the disc equals its radius. Find the distance of the line from the centre.
Because of the friction between the water in oceans with the earth's surface the rotational kinetic energy of the earth is continuously decreasing. If the earth's angular speed decreases by 0⋅0016 rad/day in 100 years find the average torque of the friction on the earth. Radius of the earth is 6400 km and its mass is 6⋅0 × 1024 kg.
Suppose the rod in the previous problem has a mass of 1 kg distributed uniformly over its length.
(a) Find the initial angular acceleration of the rod.
(b) Find the tension in the supports to the blocks of mass 2 kg and 5 kg.
A metre stick weighing 240 g is pivoted at its upper end in such a way that it can freely rotate in a vertical place through this end (see the following figure). A particle of mass 100 g is attached to the upper end of the stick through a light string of length 1 m. Initially, the rod is kept vertical and the string horizontal when the system is released from rest. The particle collides with the lower end of the stick and sticks there. Find the maximum angle through which the stick will rise.
A sphere of mass m rolls on a plane surface. Find its kinetic energy at an instant when its centre moves with speed \[\nu.\]
