Advertisements
Advertisements
प्रश्न
A hollow sphere and a solid sphere having same mss and same radii are rolled down a rough inclined plane.
विकल्प
The hollow sphere reaches the bottom first.
The solid sphere reaches the bottom with greater speed
The solid sphere reaches the bottom with greater kinetic energy.
The two spheres will reach the bottom with same linear momentum.
Advertisements
उत्तर
The solid sphere reaches the bottom with greater speed.
Acceleration of a sphere on the incline plane is given by
\[a = \frac{g\sin\theta}{1 + \frac{I_{COM}}{m r^2}}\]
\[ I_{COM}\] for a solid sphere \[= \frac{2}{5}m r^2 \]
\[\text{So, }a = \frac{g\sin\theta}{1 + \frac{2m r^2}{5m r^2}} = \frac{5}{7}g\sin\theta\]
\[I_{COM}\] for a hollow sphere \[= \frac{2}{3}m r^2 \]
\[\text{So, }a' = \frac{g\sin\theta}{1 + \frac{2m r^2}{3m r^2}} = \frac{3}{5}g\sin\theta\]
The acceleration of the solid sphere is greater; therefore, it will reach the bottom with greater speed.
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.
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 _______.
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 sphere can roll on a surface inclined at an angle θ if the friction coefficient is more than \[\frac{2}{7}g \tan\theta.\] Suppose the friction coefficient is \[\frac{1}{7}g\ tan\theta.\] If a sphere is released from rest on the incline, _____________ .
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 pendulum consisting of a massless string of length 20 cm and a tiny bob of mass 100 g is set up as a conical pendulum. Its bob now performs 75 rpm. Calculate kinetic energy and increase in the gravitational potential energy of the bob. (Use π2 = 10)
The speed of a solid sphere after rolling down from rest without sliding on an inclined plane of vertical height h is, ______
What is the condition for pure rolling?
What is the difference between sliding and slipping?
The power (P) is supplied to rotating body having moment of inertia 'I' and angular acceleration 'α'. Its instantaneous angular velocity is ______.
A ring and a disc roll on horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is 4 J then total kinetic energy of the disc is ______.
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 kinetic energy and angular momentum of a body rotating with constant angular velocity are E and L. What does `(2E)/L` represent?
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)
