A block of mass M is placed inside a smooth horizontal cylinder of radius r whose axis is kept horizontally. initially system was at rest now cylinder is given a constant acceleration 2g in the horizontal direction by an external agent. What will be the maximum angular displacement of the block with the vertical ?
Solutions:
When cylinder will move in forward direction with acceleration ‘2g’ a pseudo force will act on block kept inside cylinder, due to which block will displace slightly backward and their will be some angular displacement from vertical.
pseudo force = ma = m(2g)
at equilibrium condition, horizontal force must be balanced and vertical force also.
in horizontal direction, ma = R sinθ ……………..(1)
in vertical direction, mg = R cosθ …………….(2)
dividing equation (1) by equation (2)
ma / mg = R sinθ / R cosθ
a / g = tanθ
here, a = 2g given
2g / g = tanθ
tanθ = 2
θ = tan-1 2
Table of Contents
A block of mass M is placed inside a smooth horizontal cylinder of radius r whose axis is kept horizontally. initially system was at rest now cylinder is given a constant acceleration 2g , A block of mass M is placed inside a smooth horizontal cylinder of radius r whose axis is kept horizontally. initially system was at rest now cylinder is given a constant acceleration 2g