Question

A solid cylinder and a solid sphere having the same mass and radius roll down on the same smooth inclined plane. The ratio of the acceleration of the cylinder \((a_c)\) to that of the sphere \((a_s)\) is

• A. \(\frac{14}{15}\)
• B. \(\frac{15}{14}\)
• C. \(\frac{13}{14}\)
• D. \(\frac{11}{15}\)

Hint:

Use a = g sin(theta) / (1 + K squared over R squared).

Answer 1

The Correct Option is A

Step 1: Energy approach:
$mgh = \frac12 mv^2\left(1 + \frac{K^2}{R^2}\right)$, so $v^2 \propto \frac{1}{1 + K^2/R^2}$ and $a \propto \frac{1}{1 + K^2/R^2}$.

Step 2: Ratio:
$\frac{a_c}{a_s} = \frac{1 + 2/5}{1 + 1/2} = \frac{7/5}{3/2} = \frac{14}{15}$.

Final Answer:
The ratio is $\frac{14}{15}$, option (A). \[ \boxed{\frac{14}{15}} \]