KVPY2016PhysicsRotational Motion
A uniform metal plate shaped like a triangle ABC has a mass of 540 gm . the length of the sides AB , BC and CA are 3 ~cm , 5 ~cm and 4 ~cm , respectively. The plate is pivoted freely about the point A . What mass must be added to a vertex, so that the plate can hang with the long edge horizontal ?
Options
- A140 gm at C
- B540 gm at C
- C140 gm at B
- D540 gm at B
Correct answer
A. 140 gm at C
Step-by-step solution
CM of triangular plate is on the median. If we put a mass say m ₁ on C it will produce torque about A which balance the torque produce m g about A . Thus plate will can be in equilibrium position array l m ₁ ~g 4 37= mg y m ₁ ~g 4 4 5 = mg y m ₁= m y 5 16 m ₁ ~m = y 5 16 y < 3 m ₁ ~m < 1 ~m ₁ < m m ₁ < 540 ~g array from given option Ans. (A)