Question

A smooth inclined plane having angle of inclination ${30}^o$ with horizontal has a mass $2.5$ kg held by a sprang 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. $14.14$

Answer 1

The correct option is D $14.14$

R.E.F image

before taping upward

$mg\sin \theta =k.n\to$ As we know

$2.5\times 10\times \frac{1}{2}=k.2.5\times {10}^{-2}$

$k=5\times {10}^2$ $\sin {30}^{\circ }=\frac{1}{2}$

$k=500$

$\omega =\sqrt{\frac{k}{m}}\to$ As we know

$\omega =\sqrt{\frac{500}{2.5}}=\sqrt{200}=14.14$

$\omega =14.14\to$ Required answer