Advertisements
Advertisements
प्रश्न
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 ___________ .
विकल्प
the solid sphere
the hollow sphere
the disc
all will take same time
उत्तर
all will take same time
Let θ be the inclination angle.
From the free body diagram, we have
\[N = mg\cos\theta ..........(1)\]
\[ma = mg\sin\theta - f_r ............(2)\]
\[\text{Putting }f_r = \mu N\text{ in (2) we get,}\]
\[a = g\left( \sin\theta - \mu\cos\theta \right)\]
The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling; therefore, all the bodies come down with the same acceleration.
APPEARS IN
संबंधित प्रश्न
A thin circular ring of mass M and radius r is rotating about its axis with an angular speed ω. Two particles having mass m each are now attached at diametrically opposite points. The angular speed of the ring will become
A wheel of radius 20 cm is pushed to move it on a rough horizontal surface. If is found to move through a distance of 60 cm on the road during the time it completes one revolution about the centre. Assume that the linear and the angular accelerations are uniform. The frictional force acting on the wheel by the surface is ______________________ .
A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of a smooth incline and released. 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 ___________ .
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.
Particles of masses 1 g, 2 g, 3 g, .........., 100 g are kept at the marks 1 cm, 2 cm, 3 cm, ..........., 100 cm respectively on a metre scale. Find the moment of inertia of the system of particles about a perpendicular bisector of the metre scale.
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 surface density (mass/area) of a circular disc of radius a depends on the distance from the centre as [rholeft( r right) = A + Br.] Find its moment of inertia about the line perpendicular to the plane of the disc thorough its 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.
The following figure shows two blocks of mass m and M connected by a string passing over a pulley. The horizontal table over which the mass m slides is smooth. The pulley has a radius r and moment of inertia I about its axis and it can freely rotate about this axis. Find the acceleration of the mass M assuming that the string does not slip on the pulley.
A small spherical ball is released from a point at a height h on a rough track shown in the following figure. Assuming that it does not slip anywhere, find its linear speed when it rolls on the horizontal part of the track.
