A vehicle of mass $$200 \mathrm{~kg}$$ is moving along a levelled curved road of radius $$70 \mathrm{~m}$$ with angular velocity of $$0.2 ~\mathrm{rad...

A coin placed on a rotating table just slips when it is placed at a distance of $$1 \mathrm{~cm}$$ from the center. If the angular velocity of the tab...

As shown in the figure, a particle is moving with constant speed $$\pi ~\mathrm{m} / \mathrm{s}$$. Considering its motion from $$\mathrm{A}$$ to $$\ma...

A child of mass $$5 \mathrm{~kg}$$ is going round a merry-go-round that makes 1 rotation in $$3.14 \mathrm{~s}$$. The radius of the merry-go-round is ...

A particle is moving with constant speed in a circular path. When the particle turns by an angle $$90^{\circ}$$, the ratio of instantaneous velocity t...

A small block of mass $$100 \mathrm{~g}$$ is tied to a spring of spring constant $$7.5 \mathrm{~N} / \mathrm{m}$$ and length $$20 \mathrm{~cm}$$. The ...

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{...

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 ...

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 $$x=+2~\mathrm{m}$$, ...

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...

A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massle...

A body of mass 200g is tied to a spring of spring constant 12.5 N/m, while the other end of spring is fixed at point O. If the body moves about O in a...

A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a speed v. Which of the followin...

A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is $$60 \mathrm{~m}$$, then the magnitude of displa...

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k2rt2,...

A stone tide to a spring of length L is whirled in a vertical circle with the other end of the spring at the centre. At a certain instant of time, the...

A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction...

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 perpendi...

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 (...

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, w...

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 tens...

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...

A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that $$r = {...

The normal reaction 'N' for a vehicle of 800 kg mass, negotiating a turn on a 30$$^\circ$$ banked road at maximum possible speed without skidding is _...

A particle of mass m moves in a circular orbit under the central potential field, $$U(r) = - {C \over r}$$, where C is a positive constant. The corre...

A modern grand - prix racing car of mass m is travelling on a flat track in a circular arc of radius R with a speed v. If the coefficient of static fr...

Statement I : A cyclist is moving on an unbanked road with a speed of 7 kmh$$-$$1 and takes a sharp circular turn along a path of radius of 2m without...

A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 cm. If the block takes 40 s to...

A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inve...

A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the tip of the hand (in units of ms–2) is of the order of...

A bead of mass m stays at point P(a, b) on a wire bent in the shape of a parabola y = 4Cx2 and rotating with angular speed $$\omega $$ (see figure). T...

A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length $$\ell $$. The other end is fixed. The syste...

A smooth wire of length 2$$\pi $$r is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotat...

A particle is moving along a circular path with a constant speed of 10 ms–1. What is the magnitude of the change in velocity of the particle, when it ...

A body is projected at t = 0 with a velocity 10 ms–1 at an angle of 60o with the horizontal. The radius of curvature of its trajectory at t = 1s is R...

A disc rotates about its axis of symmetry in a horizontal plane at a steady rate of $$3.5$$ revolutions per second. A coin placed at a distnce of 1.25...

A conical pendulum of length 1 m makes an angle $$\theta $$ = 45o w.r.t. Z-axis and moves in a circle in the XY plane. The radius of the circle is 0.4...

Two cars of masses m1 and m2 are moving in circles of radii r1 and r2, respectively. Their speeds are such that they make complete circles in the same...

For a particle in uniform circular motion the acceleration $$\overrightarrow a $$ at a point P(R, θ) on the circle of radius R is (here θ is measured ...

A point $$P$$ moves in counter-clockwise direction on a circular path as shown in the figure. The movement of $$P$$ is such that it sweeps out a lengt...

Which of the following statements is FALSE for a particle moving in a circle with a constant angular speed?

The minimum velocity (in $$m{s^{ - 1}}$$) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction $$0.6$$ to av...

A stone tied to $180 \mathrm{~cm}$ long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration...

A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The...

A person starts his journey from centre 'O' of the park and comes back to the same position following path OPQO as shown in the figure. The radius of ...

A pendulum of length 2 m consists of a wooden bob of mass 50 g. A bullet of mass 75 g is fired towards the stationary bob with a speed v. The bullet e...

A curved in a level road has a radius 75 m. The maximum speed of a car turning this curved road can be 30 m/s without skidding. If radius of curved ro...

A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string are i...