Circular Motion

A huge circular arc of length 4.4 ly subtends an angle '4s' at the centre of the circle. How long it would take for a body to complete 4 revolution if its speed is 8 AU per second? Given : 1 ly = 9.46 $\times$ 10¹⁵ m 1 AU = 1.5 $\times$ 10¹¹ m

A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $\mu$. The beaker will revolve with the disc if :

For a particle in uniform circular motion, the acceleration $\overrightarrow a$ at any point P(R, $\theta$) on the circular path of radius R is (when $\theta$ is measured from the positive x-axis and v is uniform speed) :

A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is

A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be :

A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N. If the maximum speed with which the stone can revolve is ${K \over \pi }$ rev./min. The value of K is : (Assume the string is massless and unstretchable)

A stone of mass $1 \mathrm{~kg}$ is tied to end of a massless string of length $1 \mathrm{~m}$. If the breaking tension of the string is $400 \mathrm{~N}$, then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is :

A body is moving with constant speed, in a circle of radius $10 \mathrm{~m}$. The body completes one revolution in $4 \mathrm{~s}$. At the end of 3rd second, the displacement of body (in $\mathrm{m}$ ) from its starting point is :

An object moves at a constant speed along a circular path in a horizontal plane with center at the origin. When the object is at $x=+2~\mathrm{m}$, its velocity is $\mathrm{ - 4\widehat j}$ m/s. The object's velocity (v) and acceleration (a) at $x=-2~\mathrm{m}$ will be

A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if friction between tyres and road is 0.34. [take g = 10 ms$^{-2}$]