KVPY SA Exam 2016 Question Paper

Question : 68 of 80

Marks: +1, -0

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 ?

140 gm at C
540 gm at C
140 gm at B
540 gm at B

Validate

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 mg about A. Thus plate will can be in equilibrium position

m_1g × 4 \cos 37 = mg × y

m_1g × 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

from given option Ans. (A)

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