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551.

Two boys support by the ends a uniform rod of mass M and length 2L. The rod is horizontal. The two boys decided to change the ends of the rod by throwing the rod into air and catching it. The boys do not move from their position and the rod remained horizontal throughout its flight. Find the minimum impulse applied by each boy on the rod when it was thrown

Answer» Correct Answer - `(M)/(2) sqrt((pi Lg)/(3))`
Discussion
552.

A uniform rod of mass m and length 2L on a smooth horizontal surface. A particle of mass m is connected to a string of length L whose other end is connected to the end ‘A’ of the rod. Initially the string is held taut perpendicular to the rod and the particle is given a velocity `v_(0)` parallel to the initial position of the rod. (a) Calculate the acceleration of the centre of the rod immediately after the particle is projected. (b) The particle strikes the centre of the rod and sticks to it. Calculate the angular speed of the rod after this.

Answer» Correct Answer - (a) `(v_(0)^(2))/(5L)`
(b) `(3)/(2) (v_(0))/(L)`
Discussion
553.

A solid sphere is rolling on a frictionless surface, shown in figure with a translational velocity `v m//s`. If it is to climb the inclined surface then `v` should be : A. `ge sqrt((10)/(7)gh)`B. `ge sqrt(2gh)`C. `2gh`D. `(10)/(7)gh`

Answer» `(1)/(2)mv^(2)(1+k^(2)//R^(2))=mgh`
`(1)/(2)mv^(2)(1+(2)/(5))=mgh`
`(7)/(10)mv^(2)=mgh`
`v=sqrt((10gh)/(7))`
`vgesqrt((10gh)/(7))`
Discussion