IMO Practice Test: System of Particles and Rotational Motion | Class 11 Physics

Question 1 of 12

Two masses $m$ and $3m$ are joined by a light rod of length $L$. The CM lies at a distance from $m$ of:

$\frac{L}{4}$

$\frac{L}{2}$

$\frac{3L}{4}$

$\frac{L}{3}$

Explanation: $x_{cm}=\frac{3m\cdot L}{4m}=\frac{3L}{4}$ from $m$.

Question 2 of 12

A 5 kg body at rest explodes into two pieces of 2 kg and 3 kg. The 2 kg piece moves at $9\ \text{m/s}$. The 3 kg piece's speed is:

$4\ \text{m/s}$

$6\ \text{m/s}$

$9\ \text{m/s}$

$13.5\ \text{m/s}$

Explanation: Momentum conservation: $3v=2\times9\Rightarrow v=6\ \text{m/s}$ (opposite direction).

Question 3 of 12

A ring of mass $M$, radius $R$ has $I=MR^2$ about its centre. Its moment of inertia about a diameter is:

$MR^2$

$\frac{1}{2}MR^2$

$\frac{1}{4}MR^2$

$2MR^2$

Explanation: By the perpendicular axis theorem $I_z=2I_d$, so $I_d=\frac{1}{2}MR^2$.

Question 4 of 12

A wire of moment of inertia is bent... A rod of mass $M$, length $L$ has $I=\frac{1}{12}ML^2$ about its centre. About one end it is:

$\frac{1}{12}ML^2$

$\frac{1}{6}ML^2$

$\frac{1}{3}ML^2$

$ML^2$

Explanation: Parallel axis: $I=\frac{1}{12}ML^2+M(L/2)^2=\frac{1}{3}ML^2$.

Question 5 of 12

A disc and a ring of the same mass and radius have moments of inertia in the ratio (disc : ring):

$1:1$

$1:2$

$2:1$

$2:5$

Explanation: $\frac{1}{2}MR^2 : MR^2 = 1:2$.

Question 6 of 12

A torque of $4\ \text{N m}$ acts for 3 s on a wheel ($I=2\ \text{kg m}^2$) initially at rest. Its final angular speed is:

$3\ \text{rad/s}$

$6\ \text{rad/s}$

$8\ \text{rad/s}$

$12\ \text{rad/s}$

Explanation: $\alpha=\tau/I=2\ \text{rad/s}^2$; $\omega=\alpha t=2\times3=6\ \text{rad/s}$.

Question 7 of 12

A solid sphere rolling without slipping has its total KE split as (translational : rotational):

$1:1$

$5:2$

$2:5$

$2:7$

Explanation: Trans $=\frac{1}{2}mv^2$, rot $=\frac{1}{2}\cdot\frac{2}{5}mv^2$; ratio $1:\frac{2}{5}=5:2$.

Question 8 of 12

A disc rolling without slipping has the fraction of total KE that is rotational equal to:

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{2}{5}$

$\frac{2}{7}$

Explanation: Rot $=\frac{1}{2}\cdot\frac{1}{2}mv^2$; total $=\frac{3}{4}mv^2$; fraction $=\frac{1/4}{3/4}=\frac{1}{3}$.

Question 9 of 12

The acceleration of a solid sphere rolling down an incline of angle $\theta$ is:

$g\sin\theta$

$\frac{5}{7}g\sin\theta$

$\frac{2}{3}g\sin\theta$

$\frac{1}{2}g\sin\theta$

Explanation: $a=\frac{g\sin\theta}{1+2/5}=\frac{5}{7}g\sin\theta$.

Question 10 of 12

A skater with $L$ conserved triples the angular speed by changing $I$ to:

$3I$

$I/3$

$9I$

$I/9$

Explanation: $I\omega$ constant; to triple $\omega$, $I$ must become $I/3$.

Question 11 of 12

A particle moves in a straight line not through the origin at constant velocity. Its angular momentum about the origin:

increases

decreases

stays constant

is zero

Explanation: $L=mvd$ with the perpendicular distance $d$ constant, so $L$ is constant.

Question 12 of 12

A hollow and a solid sphere of equal mass and radius roll down the same incline. The faster one at the bottom is the:

hollow sphere

solid sphere

both equal

depends on mass

Explanation: Solid sphere has smaller $k^2/R^2$ ($\frac{2}{5}$ vs $\frac{2}{3}$), so larger $v$.

IMO Practice Test — System of Particles and Rotational Motion