Two particles of equal masses are revolving in circular paths of radii {r₁} and {r₂} respectivel

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3-2.Motion in Plane

easy

Two particles of equal masses are revolving in circular paths of radii ${r_1}$ and ${r_2}$ respectively with the same speed. The ratio of their centripetal forces is

A$\frac{{{r_2}}}{{{r_1}}}$

B$\sqrt {\frac{{{r_2}}}{{{r_1}}}} $

C${\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2}$

D${\left( {\frac{{{r_2}}}{{{r_1}}}} \right)^2}$

Solution

(a)$F = \frac{{m{v^2}}}{r}.$ If $m$ and $v$ are constants then
$F \propto \frac{1}{r}$
$\frac{{{F_1}}}{{{F_2}}} = \left( {\frac{{{r_2}}}{{{r_1}}}} \right)$

Standard 11

Physics

A string of length $L$ is fixed at one end and carries a mass $M$ at the other end. The string makes $2/\pi$ revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is

medium

One end of a string of length $l$ is connected to a particle of mass $m$ and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $v$ the net force on the particle (directed towards the centre) is :
$(i) \;T,$ $(ii)\; T-\frac{m v^{2}}{l},$ $(iii)\;T+\frac{m v^{2}}{l},$ $(iv) \;0$
$T$ is the tension in the string. [Choose the correct alternative].

medium

A mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity ${\omega _0}$. If the length of the string and angular velocity are doubled, the tension in the string which was initially ${T_0}$ is now

easy

(AIIMS-1985)

A ball of mass $0.25\, kg$ attached to the end of a string of length $1.96 \,m$ is moving in a horizontal circle. The string will break if the tension is more than $25 \,N$. ………. $m/s$ is the maximum speed with which the ball can be moved

easy

(AIPMT-1998)

A particle is describing circular motion in a horizontal plane in contact with the smooth inside surface of a fixed right circular cone with its axis vertical and vertex down. The height of the plane of motion above the vertex is $h$ and the semivertical angle of the cone is $\alpha $ . The period of revolution of the particle

hard

Two particles of equal masses are revolving in circular paths of radii ${r_1}$ and ${r_2}$ respectively with the same speed. The ratio of their centripetal forces is

Solution

Similar Questions

A string of length $L$ is fixed at one end and carries a mass $M$ at the other end. The string makes $2/\pi$ revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is

A mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity ${\omega _0}$. If the length of the string and angular velocity are doubled, the tension in the string which was initially ${T_0}$ is now

A ball of mass $0.25\, kg$ attached to the end of a string of length $1.96 \,m$ is moving in a horizontal circle. The string will break if the tension is more than $25 \,N$. ………. $m/s$ is the maximum speed with which the ball can be moved

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