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Applied Mechanics - Engineering

Q1:

A sphere is resting on two planes BA and BC which are inclined at 45° and 60° respectively with the horizontal. The reaction on the plane BA will be

A less than that on BC

B more than that of BC

C equal to that on BC

D zero

E none of these.

ANS:B - more than that of BC

In the case described:

  • Plane BA is inclined at 45° with the horizontal.
  • Plane BC is inclined at 60° with the horizontal.
Given that the force of gravity acts vertically downward on the sphere, the components of the weight acting perpendicular to each plane are different due to the different inclinations. Let's analyze:
  1. Plane BA (Inclined at 45°): The vertical component of the weight of the sphere acting perpendicular to plane BA is less compared to that of plane BC because the angle of inclination is smaller.
  2. Plane BC (Inclined at 60°): The vertical component of the weight of the sphere acting perpendicular to plane BC is larger compared to that of plane BA because the angle of inclination is larger.
So, the reaction force on plane BC will be greater than that on plane BA due to the larger vertical component of the weight of the sphere.