With what frequency should a particle of mass | vedclass

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

Question

(A) For the mass $M$ to remain stationary,the tension $T$ in the string must balance its weight. Therefore,$T = Mg$.This tension $T$ also provides the

Vedclass · Accepted Answer

$\frac{1}{{2\pi }}\sqrt {\frac{{Mg}}{{m\;l}}} $

Vedclass · Answer

(A) For the mass $M$ to remain stationary,the tension $T$ in the string must balance its weight. Therefore,$T = Mg$.This tension $T$ also provides the necessary centripetal force for the mass $m$ rotating in a circle of radius $l$ with frequency $n$. The centripetal force is given by $F_c = m \omega^2 l = m(2\pi n)^2 l = m 4\pi^2 n^2 l$.Equating the tension to the centripetal force: $m 4\pi^2 n^2 l = Mg$.Solving for the frequency $n$: $n^2 = \frac{Mg}{4\pi^2 ml}$.Taking the square root on both sides: $n = \frac{1}{2\pi} \sqrt{\frac{Mg}{ml}}$.

With what frequency should a particle of mass $m$ be rotated so that a body of mass $M$ remains stationary?

Similar Questions

$A$ vehicle of mass $200\,kg$ is moving along a levelled curved road of radius $70\,m$ with an angular velocity of $0.2\,rad/s$. The centripetal force acting on the vehicle is $.........\,N$.

$A$ particle describes a horizontal circle of radius $r$ in a conical funnel with a smooth inner surface with a speed of $v = 0.5 \text{ m/s}$. The height $h$ of the plane of the circle from the vertex of the funnel is (acceleration due to gravity, $g = 10 \text{ m/s}^2$): (in $\text{ cm}$)

$A$ string breaks if its tension exceeds $10 \, N$. $A$ stone of mass $250 \, g$ tied to this string of length $10 \, cm$ is rotated in a horizontal circle. The maximum angular velocity of rotation can be .......... $rad/s$.

$A$ particle of mass $m$ is rotating in a plane in a circular path of radius $r$. Its angular momentum is $L$. The centripetal force acting on the particle is:

$A$ $500 \,kg$ car takes a round turn of radius $50 \,m$ with a velocity of $36 \,km/h$. The centripetal force is (in $\,N$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module