A uniform ball of mass M and radius R can rotate freely about any axis through its centre. Its angular velocity vector is directed along positive x axis. A bullet is fired along negative Z direction and it pierces through the ball along a line that is at a perpendicular distance`r (le R)` from the centre of the ball. The bullet passes quickly and its net effect is that it applies an impulse on the ball. Mass of the bullet is m and its velocity charges from u to`v (le u)` as it passes through the ball. As a result the ball stops rotating about X axis and begins to rotate about y axis. The angular speed of the ball before and after the hit is `omega`. Find `r`.

A uniform ball of mass M and radius R can rotate freely about any axis

1.	A uniform ball of mass M and radius R can rotate freely about any axis through its centre. Its angular velocity vector is directed along positive x axis. A bullet is fired along negative Z direction and it pierces through the ball along a line that is at a perpendicular distance`r (le R)` from the centre of the ball. The bullet passes quickly and its net effect is that it applies an impulse on the ball. Mass of the bullet is m and its velocity charges from u to`v (le u)` as it passes through the ball. As a result the ball stops rotating about X axis and begins to rotate about y axis. The angular speed of the ball before and after the hit is `omega`. Find `r`.
Answer» Correct Answer - `(2sqrt2)/(5) (MR^(2) omega)/(m (u - v))`

Discussion

No Comment Found

Related InterviewSolutions

A solid cylinder and a sphere, having the same mass, rolls without slipping with the same linear velocity. If the kinetic energy of the cylinder is `75 J`, that of the sphere must beA. `60 J`B. `70 J`C. `80 J`D. `90 J`
The M.I. of solid sphere of mass M and radius R about its diameter isA. `(2)/(5) MR^(2)`B. `(7)/(5)MR^(2)`C. `(2)/(3)MR^(2)`D. `(5)/(3)MR^(2)`
If a solid sphere of mass 500 gram rolls without slipping with a velocity of 20 cm/s, then the rolling kinetic energy of the sphere will beA. 140 JB. 280 JC. 0.014 JD. 0.028 J
If I is the M.I. of a solid sphere about an axis parallel to a diameter of the sphere and at a distance x from it, which of following graphs represents the variation of I with xA. B. C. D.
A disc is rotaing with an angular velocity `omega_(0)`. A constant retarding torque is applied on it to stop the disc. The angular velocity becomes `(omega_(0))/(2)` after n rotations. How many more rotations will it make before coming to rest ?A. nB. 2nC. `(n)/(2)`D. `(n)/(3)`
The M.I. of a solid cylinder about its axis is I. It is allowed to rool down an incline plane without slipping. If its angular velocity at the bottom be `omega`, then kinetic energy of rolling cylinder will beA. `I omega^(2)`B. `(3)/(2)I omega^(2)`C. `2 I omega^(2)`D. `(1)/(2)I omega^(2)`
If a disc of mass 400 gm is rolling on a horizontal surface with uniform speed of 2 m/s, then its rolling kinetic energy will beA. 0.12 JB. 1.2 JC. 120 JD. 12 J
A rigid and a disc of different masses are rotating with the same kinetic energy. If we apply a retarding torque `tau` on the ring, it stops after making n revolution. After how many revolutions will the disc stop, if the retarding torque on it is also `tau` ?A. nB. 2nC. 4nD. n/2
If the torque acting on a system is zero then, which of the followin quantities is conserced ?A. linear momentumB. angular momentumC. moment of inertiaD. angular velocity
The dimensions of torque are :A. `[L^(3)M^(0)T^(-2)]`B. `[L^(2)M^(2)T^(-3)]`C. `[L^(2)M^(1)T^(-2)]`D. `[L^(2)M^(-1)T^(-3)]`

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment