Question

A smooth inclined plane having angle of inclination ${30}^0$ with horizontal has a mass $2.5$ kg held by a spring which is fixed at the upper end. If the mass is taken $2.5$ cm up along the surface of the inclined plane, the tension in the spring reduces to zero. If the mass is then released, the angular frequency of oscillation in radian per second

• A. $0.707$
• B. $7.07$
• C. $1.414$
• D. $14.14$

Answer 1

The correct option is D $14.14$

In the equilibrium condition,

$mgsin{30}^o=kx$

Now, $\omega =\sqrt{\frac{k}{m}}=\sqrt{\frac{gsin{30}^o}{x}}=\sqrt{\frac{10\times 1/2}{2.5}}=14.14/sec$