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प्रश्न
The speed of a solid sphere after rolling down from rest without sliding on an inclined plane of vertical height h is, ______
विकल्प
`sqrt(4/3 gh)`
`sqrt(10/7 gh)`
`sqrt(2 gh)`
`sqrt(1/2gh)`
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उत्तर
The speed of a solid sphere after rolling down from rest without sliding on an inclined plane of vertical height h is, `underline(sqrt(10/7 gh))`.
APPEARS IN
संबंधित प्रश्न
Prove the result that the velocity v of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height h is given by `v^2 = (2gh)/((1+k^2"/"R^2))`.
Using dynamical consideration (i.e. by consideration of forces and torques). Note k is the radius of gyration of the body about its symmetry axis, and R is the radius of the body. The body starts from rest at the top of the plane.
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
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 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)
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 ____________.
A 1000 kg car has four 10 kg wheels. When the car is moving, fraction of total K.E. of the car due to rotation of the wheels about their axles is nearly (Assume wheels be uniform disc)
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 ______.
The kinetic energy and angular momentum of a body rotating with constant angular velocity are E and L. What does `(2E)/L` represent?
The angular displacement of a particle in 6 sec on a circle with angular velocity `pi/3` rad/sec is ______.
An inclined plane makes an angle 30° with the horizontal. A solid sphere rolling down an inclined plane from rest without slipping has linear acceleration ______. (g = acceleration due gravity) (sin 30° = 0.5)
