NEET (UG)

Practice Test 1 — System of Particles & Rotational Motion

12 questions • 18 minutes • auto-graded with full solutions

⏱ 18:00

0 / 12 answered

[object Object]

0 / 12

0Correct

0Wrong

0Skipped

0:00Time used

Back to Study

Section A — MCQ (Single Correct)

Question 1

Two equal masses are at $x = 2\ \text{m}$ and $x = 6\ \text{m}$. Their centre of mass is at:

Solution: Equal masses ⇒ COM at the midpoint, $4\ \text{m}$.

Question 2

A force of $5\ \text{N}$ acts perpendicular to a rod $0.4\ \text{m}$ from the pivot. Torque is:

Solution: $\tau = rF = 0.4\times5 = 2\ \text{N}\cdot\text{m}$.

Question 3

The moment of inertia of a solid sphere about a diameter is:

Solution: Solid sphere: $\tfrac{2}{5}MR^2$.

Question 4

A diver curls into a ball to:

Solution: Lower $I$ raises $\omega$ by conservation of angular momentum.

Question 5

A torque of $10\ \text{N}\cdot\text{m}$ on $I = 5\ \text{kg}\cdot\text{m}^2$ gives angular acceleration:

Solution: $\alpha = \tau/I = 10/5 = 2\ \text{rad/s}^2$.

Question 6

For a ring about its central axis, the radius of gyration is:

Solution: $I = MR^2 = Mk^2$, so $k = R$.

Question 7

A man walks across a frictionless floating boat. The COM of man + boat:

Solution: No external horizontal force ⇒ COM stays put.

Question 8

Angular momentum is conserved when the net external:

Solution: Zero net external torque ⇒ angular momentum conserved.

Section B — Assertion & Reason

Question 9

A: A solid sphere rolls down an incline faster than a ring of the same mass and radius.
R: The sphere has a smaller value of $k^{2}/R^{2}$, so less of its energy goes into rotation.

Solution: Smaller $k^2/R^2$ means more energy goes to translation — R explains A.

Question 10

A: The centre of mass of a body must lie within the material of the body.
R: Mass is distributed continuously in a rigid body.

Solution: The COM can lie outside the material (e.g. a ring), so A is false; R is a true but unrelated statement.

Question 11

A: A spinning skater speeds up on pulling in her arms.
R: Her angular momentum is conserved as her moment of inertia decreases.

Solution: $I\omega$ constant with lower $I$ raises $\omega$ — R explains A.

Question 12

A: Moment of inertia depends on the choice of axis.
R: It depends on how mass is distributed relative to the axis.

Solution: Different axes give different mass distributions, hence different $I$ — R explains A.