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KVPY SA Exam 2016 Question Paper
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© examsnet.com
Question : 68
Total: 80
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
1
g
×
4
cos
37
=
m
g
×
y
m
1
g
×
4
×
4
5
=
m
g
×
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)
© examsnet.com
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