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A solid sphere, disc and solid cylinder all of the same mass and radius are allowed to roll down (from rest) on the inclined plane, then

Asked in CBSE AIPMT 1993 · Rolling on an incline

• (1) solid sphere reaches the bottom first
• (2) solid sphere reaches the bottom last
• (3) disc will reach the bottom first
• (4) all reach the bottom at the same time

Step-by-step solution

Why the other options are wrong

• (2) comes from the sphere has the smallest (k²)/(R²), 2/5 against 1/2 for both the disc and the solid cylinder, so it is first rather than last
• (3) comes from the disc's (k²)/(R²)=1/2 is larger than the sphere's 2/5; the disc ties with the solid cylinder for second place
• (4) comes from the disc and the solid cylinder do arrive together, since both have (k²)/(R²)=1/2, but the sphere beats them both

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