A non _ uniform rod weighing 0.5N has its centre of gravity at G. It is suspended horizontally from points C and D as shown above . By two vertical strings. Distance d and y respectively from G . If the tensions in the strings are M and T . What is the value of T in terms of d and y
Let's denote the length of the rod as L. Since the rod is non-uniform, its center of gravity (G) will not be at the middle of the rod.
Considering the equilibrium of the rod, we can write the following equations:
Sum of clockwise moments about point C = Sum of anti-clockwise moments about point C
0.5N * (L - d) = T * d
Sum of clockwise moments about point D = Sum of anti-clockwise moments about point D
0.5N * (L - y) = M * y
We can solve these two equations to find T in terms of d and y.
0.5N * (L - d) = T * d
0.5N * L - 0.5N * d = T * d
0.5N * L = T * d + 0.5N * d
T * d = 0.5N * L - 0.5N * d
T * d = 0.5N * (L - d)
T = 0.5N * (L - d) / d
Similarly, we can solve the second equation to find M in terms of d and y:
0.5N * (L - y) = M * y
0.5N * L - 0.5N * y = M * y
0.5N * L = M * y + 0.5N * y
M * y = 0.5N * L - 0.5N * y
M = 0.5N * (L - y) / y
So, the value of T in terms of d and y is:
T = 0.5N * (L - d) / d