a non uniform rod is balanced as shown in the diagram given that the centre of mass of the rod is 14 cm from the and mark a what is the mass of the rod
Answers
Answer:
Given:
A non-uniform rod is balanced as shown in the diagram. Given that the center of mass of the rod is 14.0 cm from the end marked A.
To find:
Let the mass be m. Now, the gravitational force will act on the CENTRE OF MASS.
Now, since the rod is in rotational equilibrium, the net torque will be zero.
Considering the axis of rotation at the ∆:
\therefore \: \sum( \tau) = 0∴∑(τ)=0
\implies \: mg(30 - 14) - \dfrac{80}{1000} g(20) = 0⟹mg(30−14)− 100080
g(20)=0
\implies \: mg(16) - \dfrac{80}{1000} g(20) = 0⟹mg(16)− 100080
g(20)=0
\implies \: m(16) - \dfrac{80}{1000} (20) = 0⟹m(16)−
100080 (20)=0
\implies \: m(16) - \dfrac{8}{10} (2) = 0⟹m(16)−
108 (2)=0
\implies \: m(16) = \dfrac{8}{10} (2)⟹m(16)= 108
(2)\: m(2) = \dfrac{1}{10} (2)⟹m(2)= 10 (2)
\\: m = \dfrac{1}{10} \: kg⟹m= 101 kg
\implies \: m = \dfrac{1}{10} \times 1000 \: gram⟹m= 101 ×1000gram
\implies \: m = 100 \: gram⟹m=100gram
So, mass of rod is 100 grams.
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Answer:
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