A uniform wooden stick is pivoted at one of its ends about a vertical axis perpendicular to its length, allowing it to rotate freely in a horizontal plane. If the mass of the stick is 150 g and its moment of inertia about this pivot axis is 14000 g cm ^2 , the length of the stick is nearly:

Step-by-step solution

The moment of inertia of a uniform rod of mass m and length L about an axis passing through one end and perpendicular to its length is given by: I = mL^2 3 Given m = 150 g and I = 14000 g cm ^2 , substituting these values into the formula: 14000 = 150 L^2 3 14000 = 50 L^2 L^2 = 14000 50 = 280 L = 280 16.73 cm The length of the stick is nearly 16.7 cm . Answer: 16.7 cm