A mass m is tied to one end of a spring and w | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $\ell$ be the original length of the spring. Let $k$ be the spring constant.When the mass is whirled with angular velocity $\omega$,the centri

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(B) Let $\ell$ be the original length of the spring. Let $k$ be the spring constant.When the mass is whirled with angular velocity $\omega$,the centripetal force is provided by the spring tension $F = k \cdot e_1$,where $e_1 = 1 \ cm$ is the elongation.The radius of the circle is $r_1 = \ell + e_1$.Thus,$m(\ell + e_1)\omega^2 = k e_1$  --- $(1)$When the angular velocity is doubled $(2\omega)$,the elongation becomes $e_2 = 6 \ cm$.The radius of the circle is $r_2 = \ell + e_2$.Thus,$m(\ell + e_2)(2\omega)^2 = k e_2$  --- $(2)$Dividing equation $(1)$ by equation $(2)$:$\frac{m(\ell + e_1)\omega^2}{m(\ell + e_2)4\omega^2} = \frac{k e_1}{k e_2}$$\frac{\ell + 1}{4(\ell + 6)} = \frac{1}{6}$$6(\ell + 1) = 4(\ell + 6)$$6\ell + 6 = 4\ell + 24$$2\ell = 18$$\ell = 9 \ cm$.

$A$ mass $m$ is tied to one end of a spring and whirled in a horizontal circle with constant angular velocity. The elongation in the spring is $1 \ cm$. If the angular speed is doubled,the elongation in the spring is $6 \ cm$. The original length of the spring is (in $cm$)

Similar Questions

$A$ spring-block system is placed on a rough horizontal floor. The block is pulled towards the right to give the spring an elongation $x_0$ such that $\frac{\mu mg}{K} < x_0 < \frac{2\mu mg}{K}$,and then released. Which of the following statements is correct?

What is the acceleration of the block and trolley system shown in the figure,if the coefficient of kinetic friction between the trolley and the surface is $0.04$? What is the tension in the string? (Take $g = 10\; m s^{-2}$). Neglect the mass of the string.

$A$ vehicle is moving with uniform speed along $3$ different shaped roads: horizontal,concave,and convex. The surface of the road on which the normal reaction on the vehicle is maximum is

$STATEMENT-1$: It is easier to pull a heavy object than to push it on a level ground.
$STATEMENT-2$: The magnitude of frictional force depends on the nature of the two surfaces in contact.

$A$ body of mass $2 \,kg$ is acted upon by two forces each of magnitude $1 \,N$, making an angle of $60^{\circ}$ with each other. The net acceleration of the body (in $m/s^2$) is

Vedclass Test Series

Exam Paper Generator

Online Exam Module