Advertisements
Advertisements
प्रश्न
The following figure shows a smooth inclined plane fixed in a car accelerating on a horizontal road. The angle of incline θ is related to the acceleration a of the car as a = g tanθ. If the sphere is set in pure rolling on the incline, _____________.
विकल्प
it will continue pure rolling
it will slip down the plane
its linear velocity will increase
its linear velocity will slowly decrease
Advertisements
उत्तर
it will continue pure rolling
From the free body diagram of sphere, we have
Net force on the sphere along the incline,
Fnet = mgsinθ − macosθ ...(i)
On putting a = gtanθ in equation (i), we get
Fnet = 0
Therefore, if the sphere is set in pure rolling on the incline, it will continue pure rolling.
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;
For perfect rolling motion, work done against friction 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 _______.
Can an object be in pure translation as well as in pure rotation?
A cylinder rolls on a horizontal place surface. If the speed of the centre is 25 m/s, what is the speed of the highest point?
A string is wrapped over the edge of a uniform disc and the free end is fixed with the ceiling. The disc moves down, unwinding the string. Find the downward acceleration of the disc.
Discuss the interlink between translational, rotational and total kinetic energies of a rigid object rolls without slipping.
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 of mass 1 kg and radius 10 cm rolls without slipping on a horizontal surface, with velocity of 10 emfs. The total kinetic energy of sphere is ______.
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 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)
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 ______.
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 ______.
A disc of mass 4 kg rolls on a horizontal surface. If its linear speed is 3 m/ s, what is its total kinetic energy?
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)
