Two identical thin rods of mass M kg and length L m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpendicular to the plane of the rods is
x ─── 2 ML² kg m².
The value of x i $s __________.$

Question

Two identical thin rods of mass M kg and length L m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpendicular to the plane of the rods is

x ─── 2 ML² kg m².

The value of x i $s __________.$

G1 Physics · Accepted Answer

For the vertical rod, the axis passes through one end and is perpendicular to the rod. Therefore, I₍vertical₎ = ML² ───── 3 . For the horizontal rod, use the parallel-axis theorem. Its moment of inertia about its own centre is I₍CM₎ = ML² ───── 12 . The centre of the horizontal rod is at distance L from point P. Hence, I₍horizontal₎ = I₍CM₎+ML² = ML² ───── 12 +ML². Therefore, I₍total₎ = ML² ───── 3 + ML² ───── 12 + ML² = 17ML² ─────── 12 . The supplied paper prints the required form as I = x ──…

Two identical thin rods of mass M kg and length L m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpendicular to the plane of the rods is x ─── 2 ML² kg m². The value of x i s __________.