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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;
The instantaneous speed of the point of contact during rolling is zero.
If a rigid body of radius ‘R’ starts from rest and rolls down an inclined plane of inclination
‘θ’ then linear acceleration of body rolling down the plane is _______.
In rear-wheel drive cars, the engine rotates the rear wheels and the front wheels rotate only because the car moves. If such a car accelerates on a horizontal road the friction
(a) on the rear wheels is in the forward direction
(b) on the front wheels is in the backward direction
(c) on the rear wheels has larger magnitude than the friction on the front wheels
(d) on the car is in the backward direction.
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?
What is the condition for pure rolling?
A solid sphere rolls down from top of inclined plane, 7m high, without slipping. Its linear speed at the foot of plane is ______. (g = 10 m/s2)
A man is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity `omega`. The tension in the strings is F. If the length of string and angular velocity are doubled, the tension in string is now ____________.
The power (P) is supplied to rotating body having moment of inertia 'I' and angular acceleration 'α'. Its instantaneous angular velocity is ______.
A solid spherical ball rolls on an inclined plane without slipping. The ratio of rotational energy and total energy 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 ______.
