A rod of mass 2M, length L is kept stationary with the help of a chain and ideal string as shown in figure. The chain is suspended symmetrically at both ends and mass of chain is 2M. For equilibrium the tension in string is given as T=17ηMg/9 (Newton). Find the value of η.
Physics · Mixed Chapter
JEE Mains

Question

A rod of mass 2M, length L is kept stationary with the help of a chain and ideal string as shown in figure. The chain is suspended symmetrically at both ends and mass of chain is 2M. For equilibrium the tension in string is given as T=17ηMg/9 (Newton). Find the value of η.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The rod weight 2Mg acts at its midpoint. The chain of total weight 2Mg is supported at its two ends; for a symmetric hanging chain, each end has an upward vertical tension component Mg. Step 2: Resolve chain tension along the direction making 37° in the figure and string tensions at the rod's endpoints. Use sin37°=3/5 and cos37°=4/5. Step 3: Impose zero net torque about the left rod support, then horizontal and vertical force balance at the right-hand joint. The given geometry leads to…