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प्रश्न
A uniform disc of mass 100g has a diameter of 10 cm. Calculate the total energy of the disc when rolling along with a horizontal table with a velocity of 20 cms-1. (take the surface of the table as reference)
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उत्तर
Mass of the disc = 100 g = 100 x 10-3 kg = `1/10`kg
Velocity of disc = 20 cm s-1 = 20 x 10-2 ms-1 = 0.2 ms-1
r = 5 cm = `5 xx 10^-2 m, omega = v/r = (20 xx 10^-2)/(5 xx 10^-2) = 4`
Energy = `1/2mV^2 + 1/2Iomega^2 = 1/2(mV^2 + Iomega^2),` where I = `1/2mr^2`
= `1/2[1/10 xx 0.2 xx 0.2 + 1/2 xx 1/10 xx 25 xx 1/10^4 xx 16]`
= `1/2[4/1000 + 2/1000] = 1/2[6/1000]`
Energy = `3 xx 10^-3` J
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संबंधित प्रश्न
Read each statement below carefully, and state, with reasons, if it is true or false;
For perfect rolling motion, work done against friction is zero.
Read each statement below carefully, and state, with reasons, if it is true or false;
A wheel moving down a perfectly frictionless inclined plane will undergo slipping (not rolling) motion
Two uniform solid spheres having unequal masses and unequal radii are released from rest from the same height on a rough incline. If the spheres roll without slipping, ___________ .
A solid sphere of mass 0⋅50 kg is kept on a horizontal surface. The coefficient of static friction between the surfaces in contact is 2/7. What maximum force can be applied at the highest point in the horizontal direction so that the sphere does not slip on the surface?
Answer in Brief:
A rigid object is rolling down an inclined plane derive the expression for the acceleration along the track and the speed after falling through a certain vertical distance.
A solid sphere is rolling on a frictionless surface with translational velocity 'V'. It climbs the inclined plane from 'A' to 'B' and then moves away from Bon the smooth horizontal surface. The value of 'V' should be ______.
A circular disc reaches from top to bottom of an inclined plane of length 'L'. When it slips down the plane, it takes time ' t1'. when it rolls down the plane, it takes time t2. The value of `t_2/t_1` is `sqrt(3/x)`. The value of x will be ______.
Solid spherical ball is rolling on a frictionless horizontal plane surface about is axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is ______.
The least coefficient of friction for an inclined plane inclined at angle α with horizontal in order that a solid cylinder will roll down without slipping is ______.
If x = at + bt2, where x is the distance travelled by the body in kilometers while t is the time in seconds, then the unit of b is ______.
