JEE Circular Motion PYQs with Video Solutions PDF

If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately :
(Take : $$g = 10$$ ms$$^{-2}$$, the radius of earth, $$R = 6400 \times 10^3$$ m, Take $$\pi = 3.14$$)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun.
Reason (R) : The moon takes less time to move around the earth than the time taken by the earth to move around the sun.
In the light of the above statements, choose the most appropriate answer from the options given below :

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is $$\omega$$ rad s$$^{-1}$$. The difference in the height, h (in cm) of liquid at the Centre of vessel and at the sides of the vessel will be:

The point $$A$$ moves with a uniform speed along the circumference of a circle of radius 0.36 m and covers 30° in 0.1 s. The perpendicular projection $$P$$ from $$A$$ on the diameter $$MN$$ represents the simple harmonic motion of $$P$$. The restoration force per unit mass when $$P$$ touches $$M$$ will be:

Two planets $$A$$ and $$B$$ of equal mass are having their period of revolutions $$T_A$$ and $$T_B$$ such that $$T_A = 2T_B$$. These planets are revolving in the circular orbits of radii $$r_A$$ and $$r_B$$ respectively. Which out of the following would be the correct relationship of their orbits?

A small block of mass 100 g is tied to a spring of spring constant 7.5 N m$$^{-1}$$ and length 20 cm. The other end of spring is fixed at a particular point A. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity 5 rad s$$^{-1}$$ about point A, then tension in the spring is

Two small balls with masses m and 2m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this system is L about an axis (A) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about A is :

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$$^{-1}$$ without skidding. If radius of curved road is changed to $$48$$ m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be ______ m s$$^{-1}$$.

A string of length $$L$$ is fixed at one end and carries a mass of $$M$$ at the other end. The mass makes $$\left(\frac{3}{\pi}\right)$$ rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is $$\underline{\hspace{2cm}} ML.$$

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius $$9$$ m and completes 120 revolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in $$m/s^2$$) :

A car moving with a speed of 54 km/h takes a turn of radius 20 m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take $$g = 10$$ m/s$$^2$$)

A person moved from $$A$$ to $$B$$ on a circular path as shown in figure. If the distance travelled by him is $$60 \text{ m}$$, then the magnitude of displacement would be: (Given $$\cos 135° = -0.7$$)

One end of a massless spring of spring constant $$k$$ and natural length $$l_0$$ is fixed while the other end is connected to a small object of mass $$m$$ lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity $$\omega$$ about an axis passing through fixed end, then the elongation of the spring will be

A string of area of cross-section 4 mm$$^2$$ and length 0.5 is connected with a rigid body of mass 2 kg. The body is rotated in a vertical circular path of radius 0.5 m. The body acquires a speed of 5 m s$$^{-1}$$ at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is _____ $$\times 10^{-5}$$. (Use Young's modulus $$10^{11}$$ N m$$^{-2}$$ and $$g = 10 \ m s^{-2}$$)

A metal wire of length 0.5 m and cross-sectional area $$10^{-4}$$ m$$^2$$ has breaking stress $$5 \times 10^8$$ N m$$^{-2}$$. A block of 10 kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be _____ m s$$^{-1}$$

Consider two satellites $$S_1$$ and $$S_2$$ with periods of revolution 1hr and 8hr respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite $$S_1$$ to the angular velocity of satellite $$S_2$$ is:

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 complete one round, the normal force by the side walls of the groove is:

A satellite is launched into a circular orbit of radius $$R$$ around earth, while a second satellite is launched into a circular orbit of radius 1.02 $$R$$. The percentage difference in the time periods of the two satellites is:

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 $$r = \frac{L}{\sqrt{2}}$$. The speed of particle will be:

The minimum and maximum distances of a planet revolving around the Sun are $$x_1$$ and $$x_2$$. If the minimum speed of the planet on its trajectory is $$v_0$$, then its maximum speed will be:

A box weighs 196 N on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take g = 10 ms$$^{-2}$$ at the north pole and the radius of the earth = 6400 km):

A clock has a continuously moving second's hand of $$0.1\,\text{m}$$ length. The average acceleration of the tip of the hand (in units of $$\text{ms}^{-2}$$) is of the order of:

The mass density of a spherical galaxy varies as $$\frac{K}{r}$$ over a large distance $$r$$ from its center. In that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on R as:

A satellite is in an elliptical orbit around a planet $$P$$. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is:

A body is moving in a low circular orbit about a planet of mass M and radius R. The radius of the orbit can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is:

A satellite is revolving in a circular orbit at a height h from the earth surface, such that $$h \ll R$$ where R is the radius of the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is

If the angular momentum of a planet of mass $$m$$, moving around the Sun in a circular orbit is $$L$$, about the center of the Sun, its areal velocity is:

A body A of mass $$m$$ is moving in a circular orbit of radius $$R$$ about a planet. Another body B of mass $$\frac{m}{2}$$ collides with A with a velocity which is half $$\left(\frac{v}{2}\right)$$ the instantaneous velocity $$\vec{v}$$ of A. The collision is completely inelastic. Then, the combined body:

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 $$g = 10$$ m s$$^{-2}$$]

An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at $$x = +2$$ m, its velocity is $$-4\hat{j}$$ m s$$^{-1}$$. The object's velocity ($$v$$) and acceleration ($$a$$) at $$x = -2$$ m will be

A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the centre. If the angular velocity of the table is halved, it will just slip when placed at a distance of _______ from the centre:

A cylindrical tube $$AB$$ of length $$l$$, closed at both ends contains an ideal gas of 1 mol having molecular weight $$M$$. The tube is rotated in a horizontal plane with constant angular velocity $$\omega$$ about an axis pe1pendicular to $$AB$$ and passing through the edge at end $$A$$ , as shown in the figure. If $$P_{A}$$ and $$P_{B}$$ are the pressures at $$A$$ and $$B$$ respectively, then
(Consider the temperature is same at all points in the tube)

A circular disc has radius $$R_{1}$$ and thickness $$T_{1}$$. Another circular disc made of the same material has radius $$R_{2} and thickness $$T_{2}. If the moment of inertia of both discs are same and $$ \frac{R_{1}}{R_{2}}=2 \text { then }\frac{T_{1}}{T_{2}}=\frac{1}{\alpha} $$. The value of $$\alpha$$ is__________.

If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon =27 days and gravitational attraction between the satellite and the moon is neglected.

A satellite is launched into a circular orbit of radius $$R$$ around the earth. A second satellite is launched into an orbit of radius $$1.03R.$$ The time period of revolution of the second satellite is larger than the first one approximately by:

Four particles, each of mass $$1$$ kg are placed at four corners of a square of side $$2$$ m. The moment of inertia of the system about an axis perpendicular to its plane and passing through one of its vertex is ______ kg m$$^2$$.

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle ($$\theta$$) of thread deflection in the extreme position will be :

If the radius of curvature of the path of two particles of same mass are in the ratio $$3 : 4$$, then in order to have constant centripetal force, their velocities will be in the ratio of:

A car of $$800 \text{ kg}$$ is taking turn on a banked road of radius $$300 \text{ m}$$ and angle of banking $$30°$$. If coefficient of static friction is $$0.2$$ then the maximum speed with which car can negotiate the turn safely: $$(g = 10 \text{ m/s}^2, \sqrt{3} = 1.73)$$

A bob of mass $$m$$ is suspended by a light string of length $$L$$. It is imparted a minimum horizontal velocity at the lowest point $$A$$ such that it just completes half circle reaching the top most position $$B$$. The ratio of kinetic energies $$\frac{(K.E.)_A}{(K.E.)_B}$$ is: