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

Answer 1

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