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 as shown in figure. 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 is

• A. 0.707
• B. 7.07
• C. 1.414
• D. 14

Answer 1

The correct option is D 14

When, tension in the spring reduces to zero.

Inclined force = Restoring force

At inclination $=\theta ,$

$mgsin\theta =kx$

$2.5\times 9.8\times sin30=k\times 2.5\times {10}^{-}2$

$9.8\times 1/2=k/100$

$k=490N/m$

Angular frequency is given by,

$w=\surd \left(k/m\right)$

$w=\surd \left(490/2.5\right)$

$w=\surd 196$

$w=14rad/s$

Angular frequency is $14rad/Hz.$

Hence, the option $D$ is the correct answer.