Sindh Mdcat Exclusive Course Physics Circular Motion — Solved MCQs

Question 1

A disc, a hoop, and a sphere of the same mass and radius are rolled down from a frictionless, inclined plane. Which has a greater speed on reaching the ground?

Accepted Answer

C. Sphere — The sphere has most of its mass near the axis of rotation, so it will have the smallest moment of inertia and will reach the ground first.The disc has its mass uniformly distributed, so will have a greater moment of inertia and will arrive second.The hoop has all its mass concentrated away from the center, so will have the greatest moment of inertia. It will arrive last, but will then travel farther away on the horizontal plane than the other shapes, as it will have stored more of the original potential energy in the form of rotational energy.

Question 2

In rotatory motion, angular momentum plays a role which is analogous to that played by _ in linear motion.

Accepted Answer

B. Linear momentum — The rotational momentum and "linear momentum both form the same function in a body, they are responsible for keeping the body moving in the direction it is moving, and both quantity the amount of motion (translational tor linear momentum and rotational tor angular momentum) present in the body. Moment of inertia in an analogue to mass in rotational motion. If we want to feel inertia in linear motion we examine the linear acceleration of mass produced by a given force. If acceleration for a given force is more we say that the body has less inertia. If the same force produces less acceleration in another mass then the inertia of the second body for linear motion is large compared to the first body. The expression for this fact is F/m=a. So, mass is the measure of inertia to linear motion.

Question 3

A wheel starts rotating from the result with an angular acceleration of 2 rads-2 till its angular speed becomes 6 rad/s. The angular displacement of the wheel will be equal to:

Accepted Answer

B. 9 rad — V = u + at6 = 0 + 2tt = 3 secondsØ = ut + 1/2at2Ø = 0 + 1/2 • 2 • 3²Ø = 9 radian.

Question 4

Which of the following gives the relationship between linear velocity and angular velocity?

Accepted Answer

A. v = rω — The greater the rotation angle in a given amount of time, the greater the angular velocity. Angular velocity (ω) is analogous to linear velocity (v). We can write the relationship between linear velocity and angular velocity in two different ways: v=rω or ω=v/r.

Question 5

If the body is rotating with uniform angular velocity, then its torque is:

Accepted Answer

A. Zero — Torque will be zero because the force on the object is zero, since it is not accelerating. And also if the body is at rest or rotating with uniform angular velocity the angular acceleration will be zero in this case the torque acting on a body will be zero.Torque is given by solution i.e. torque = r.F sin (theta)Here force = maAcceleration is given by change in velocity/timeIf the change in velocity is zero, acceleration is zero, force is zero, thus torque is also zero. Any other value is not remotely possible

Question 6

Work done, due to centripetal force, for circular motion will be:

Accepted Answer

B. Zero — The displacement of an object after one complete revolution is 0 as the object returns to its original position. The beginning and final locations of a body that travels a distance and returns to its original place are the same. The displacement is zero in this situation, but the distance travelled is not.As work done = force x displacement, given that the displacement is 0, work done is also 0.

Question 7

The ratio of angular speed of moon around the Earth to its angular speed about its own axis is:

Accepted Answer

D. 1:1 — The moon orbits the Earth once every 27.322 days. In the same amount of time, the moon rotates once on its axis. As a result, the moon does not seem to be spinning but appears to observers from Earth to be keeping almost perfectly still (this is called synchronous rotation). So its angular speed (W) around its own axis isW =2π /TW(moon) = (2π)/(27.322 x 24 x 3600) = 2.67*10(-6) rad/sFor orbital motion around the earth, the angular speed isW(earth) = (2π)/(27.322 x 24 x 3600) = 2.67*10(-6) rad/sSo the ratio is 1:1

Question 8

The moment of inertia of a solid sphere of mass ‘m’ having radius ‘r’ about a line passing through its center is:

Accepted Answer

B. 2/5 mr2 — The moment of inertia of a solid sphere about a line passing through its center is given by the formula:I = (2/5)mr²where m is the mass of the sphere and r is its radius.

Question 9

1 radian = _ degrees.

Accepted Answer

D. 57.3 — Radian is the SI unit of measuring angles. It is the measure of the central angle whose arc length is the same as the radius of the circle.In one circle,2π radians =3601 radian is equal to 180/π degrees, which is approximately 57.3°

Question 10

A rotating wheel of radius 0.5 m has an angular velocity of 5 rad/s at some instant and 10 rad / s after 5 s. Find the angular acceleration of a point on its rim.

Accepted Answer

A. 1 rad/s2 — The angular acceleration of a rotating object can be found using the formula α = (ωf - ωi) / t, where ωf is the final angular velocity, ωi is the initial angular velocity, and t is the time interval. In this case, the initial angular velocity (ωi) is 5 rad/s, the final angular velocity (ωf) is 10 rad/s, and the time interval (t) is 5 seconds. Substituting these values into the formula gives: α = (10 rad/s - 5 rad/s) / 5 s = 1 rad/s2. Therefore, Option A is correct. All other options are incorrect as they do not result from applying this formula to the given values.

Question 11

When the aircraft Concorde is moving in a horizontal plane at a constant speed of 650 ms-1, its turning circle has a radius of 80 km. What is the ratio of the centripetal force to the weight of the aircraft? (g = 9.8 m/s2)

Accepted Answer

B. 0.54 — The ratio of Centripetal force to the weight of the aircraft=mv^2/r divided by mgm*(650)^2/80*1000 / m*9.81=0.54.

Question 12

A 400 gram ball is tied to the end of a cord and whirled in à horizontal circle of radius 0.6 m. If the ball makes five complete revolutions in 2 s, what is the ball's linear speed?

Accepted Answer

E. 9.42 m/s — Linear speed = Distance / TimeDistance = 5 × 2 × pi × r = 5 × 2 × 22/7 × 0.6 = 132 / 7 = 18.85 mspeed = 18.85 / 2 = 9.42 m/s

Question 13

A car going around a certain curve at a speed of 25 km/h has centripetal force of 100 N acting on it. If the speed of the car is doubled, the centripetal force:

Accepted Answer

A. Is quadrupled — The formula that will be used here will be: F=(m)(v)2/r. By doubling the speed of the car, the centripetal force should be quadrupled due to the power of 2.

Question 14

The rate of change of angular velocity with respect to _ defines angular acceleration.

Accepted Answer

D. Time — Angular acceleration is defined as the rate of change of angular velocity with respect to time. This means it describes how quickly the speed of rotation is changing, and is typically measured in radians per second squared (rad/s^2). None of the other options—speed, frequency, distance, or gravity—relate directly to this rate of change. Speed and distance are linear measures, frequency is a measure of cycles per time but not change rate, and gravity is a force, not a measure of change in motion over time.

Question 15

A body having translatory motion possesses _ and _. In the same way a body having rotatory motion possesses _ and _.

Accepted Answer

B. Linear velocity... Linear momentum... Angular velocity... Angular momentum — The correct answer is: Linear velocity... Linear momentum... Angular velocity... Angular momentum.In translatory motion, all points of a body move uniformly in a single direction, involving linear properties such as linear velocity and linear momentum. This type of motion does not change the orientation of the object.In contrast, rotatory motion occurs when a body rotates around its own axis, involving angular properties like angular velocity and angular momentum. For example, the Earth's rotation about its axis is a type of rotatory motion.All options except B do not properly align the motion types with their respective properties, which is why they are incorrect.

Question 16

When brakes of a car are applied, angular velocity of a flywheel reduces from 900 cycle / min to 720 cycle / min in 6 sec. Angular retardation is:

Accepted Answer

A. 𝝅 rad/s2 — This is the following solution.First, we need to convert the given angular velocities from cycles per minute to radians per second. We know that 1 cycle is equal to 2π radians. Therefore,Angular velocity at the start = 900 cycles/min = (900 x 2π) / 60 rad/s = 30π rad/sAngular velocity at the end = 720 cycles/min = (720 x 2π) / 60 rad/s = 24π rad/sThe time taken for the flywheel to reduce its angular velocity from 30π rad/s to 24π rad/s is 6 seconds. We can use the formula for angular retardation:Angular retardation (α) = (ω2 - ω1) / tWhere ω2 is the final angular velocity, ω1 is the initial angular velocity, and t is the time taken.Substituting the given values, we get:Angular retardation (α) = (24π - 30π) / 6 = -π rad/s^2Therefore, the angular retardation is -π rad/s^2.

Question 17

One complete circle is equal to:

Accepted Answer

A. 2π radian — There are 2π radians in a full circle. So 2π radians should equal 360°.

Question 18

A body is hanging from a rigid support by an extensible string of length L. It is struck inelastically by an identical body of mass m with horizontal velocity v =√2gl , the tension in the string increases just after striking by:

Accepted Answer

C. 2mg — Initially, the tension in the string is T = mg, which equals the weight of the hanging body. When struck by an identical body inelastically, the system's mass becomes 2m. Conservation of momentum gives us:mv = 2m(v'), thus v' = v/2.Using the inelastic collision principles, the new tension T' is given by T' - 2mg = 2m(v')^2/L. By substituting v' = v/2 and v = √(2gL), we find T' = 3mg.Therefore, the tension increase is T' - T = 3mg - mg = 2mg.Option A is incorrect as it ignores the momentum change. Option B miscalculates the velocity and resultant tension. Option D is incorrect since the calculated increase in tension is indeed 2mg, making Option C the right choice.

Question 19

If a wheel of radius r turns through an angle of 30°, then the distance through which any point on its rim moves is?

Accepted Answer

B. r(π/6) — The dispance through which any point on the rim moves is equal to the the distance the rim has rolled, S. S = rθ where θ is angle in radians Convert 30° to radians 30 x π/180 = π/6 S = r(π/6)

Question 20

A body is moving in a circle at constant speed. Which statement is true?

Accepted Answer

A. The resultant force acts towards the centre of the circle — The resultant force, being the centripetal force, always acts towards the center of the circle in situations where an object is moving in a circle, at a constant speed.

Sindh Mdcat Exclusive Course Physics Circular Motion — Solved Past Paper with Answers

More Sindh / DUHS Solved Papers