A fixed spherical mass M and two identical point masses m lie on the same straight line. The two point masses are connected by a rigid massless rod of length ℓ and can move along the line. When the nearer point mass is at r = 3ℓ from M, the rod tension is zero for m = K(M/288). Find K.

Question

G1 Physics · Accepted Answer

Step 1: When tension is zero, the two point masses must have equal acceleration while separated by ℓ. The nearer mass is at 3ℓ and the farther at 4ℓ from M. Step 2: Near mass: a₁=GM/(9ℓ²)-Gm/ℓ². Far mass: a₂=GM/(16ℓ²)+Gm/ℓ². Set a₁=a₂. Step 3: GM(1/9-1/16)=2Gm ⇒ 7M/144=2m ⇒ m=7M/288. Therefore K=7.