System of Particles and Rotational Motion Online Objective Test | System of Particles and Rotational Motion Online Objective Test

# System of Particles and Rotational Motion # CBSE 11TH PHYSICS Prepare / Learn

Q1. When a mass is rotating in a plane about a fixed point, its angular momentum is directed along

A. the radius

B. the axis of rotation

C. A line at an angle of 45o to the plane of rotation

D. The tangent to the orbit

Answer : Option B
Explaination / Solution:

$\vec{L} = \vec{r} \times \vec{p} = m (\vec{r} \times \vec{v})$ cular to both

$\vec{r}$ and $\vec{v}$ that is along the axis of rotation according to right hand screw rule.

# System of Particles and Rotational Motion # CBSE 11TH PHYSICS Prepare / Learn

Q2. When a mass is rotating in a plane about a fixed point, its angular momentum is directed along

A. the radius

B. the axis of rotation

C. A line at an angle of 45o to the plane of rotation

D. The tangent to the orbit

Answer : Option B
Explaination / Solution:

$\vec{L} = \vec{r} \times \vec{p} = m (\vec{r} \times \vec{v})$ cular to both

$\vec{r}$ and $\vec{v}$ that is along the axis of rotation according to right hand screw rule.

# System of Particles and Rotational Motion # CBSE 11TH PHYSICS Prepare / Learn

Q3. Which of the following has the largest moment of inertia?

A. Ring of mass M and radius R about an axis perpendicular to its plane

B. Bar magnet of mass M and length R about any axis passing through its centre of mass

C. Disc of mass M and radius R about an axis perpendicular to its plane

D. Solid sphere of mass M and radius R about any axis passing through its centre of mass

Answer : Option A
Explaination / Solution:

$\begin{aligned} I_{R i n g} = M R^{2} \\ I_{d i s c} = \frac{1}{2} M R^{2} \\ I_{s p h e r e} = \frac{2}{5} M R^{2} \\ I_{r o d} = \frac{M R^{2}}{12} \end{aligned}$

Hence ring has largest moment of inertia.

# System of Particles and Rotational Motion # CBSE 11TH PHYSICS Prepare / Learn

Q4. A spherical solid ball of 1 kg. mass and radius 3 cm is rotating about an axis passing through its centre with an angular velocity of 50 radians/s. The kinetic energy of rotation is

A. 910 J

B. 920 J

C. 45000 J

D. (9/20)J

Answer : Option D
Explaination / Solution:

M=1KgR=3cm=3×10−2mω=50rad/sK=12Iω2=12×25MR2×ω2K=12×25×1×(3×10−2)2×50×50=920J

# System of Particles and Rotational Motion # CBSE 11TH PHYSICS Prepare / Learn

Q5. A jet airplane travelling at the speed of 500 kmh–1 ejects its products of combustion at the speed of 1500 km h–1relative to the jet plane. What is the speed of the combustion with respect to an observer on ground?

A. -2550 km/h

B. -2000 km/h

C. -1250 km/h

D. -1000 km/h

Answer : Option D
Explaination / Solution:

Speed of the jet airplane, vjet = 500 km/h Relative speed of its products of combustion with respect to the plane, vsmoke = – 1500 km/h

Speed of its products of combustion with respect to the ground = v′smoke

Relative speed of its products of combustion with respect to the airplane, vsmoke = v′smoke – vjet

=> – 1500 = v′smoke – 500

=> v′smoke = – 1000 km/h

The negative sign indicates that the direction of its products of combustion is opposite to the direction of motion of the jet airplane.

# System of Particles and Rotational Motion # CBSE 11TH PHYSICS Prepare / Learn

Q6. If a gymnast sitting on a rotating stool with his arms outstretched, suddenly lowers his hands

A. the angular momentum increases

B. the angular velocity stays constant

C. his moment of inertia decreases

D. the angular velocity decreases

Answer : Option C
Explaination / Solution:

When gymnast lowers his hand the distance of mass from rotational axis decrease. Hence his moment of inertia decreases and angular velocity increase to conserve angular momentum.

# System of Particles and Rotational Motion # CBSE 11TH PHYSICS Prepare / Learn

Q7. A fly wheel rotating about a fixed axis has a kinetic energy of 360 joule when its angular speed is 30 radians per second. The moment of inertia of the fly wheel about the axis of rotation is

A. 0.6 kg

m^{2}

B. 0.8Kgm2

C. 0.15 kg m2

D. 0.75 kg

m^{2}

Answer : Option B
Explaination / Solution:

K=12Iω2K=360Jω=30rad/sI=2Kω2=2×36030×30=0.8Kgm2

# System of Particles and Rotational Motion # CBSE 11TH PHYSICS Prepare / Learn

Q8. A body of mass 2.0 kg and radius of gyration 0.5 m is rotating about an axis. If its angular speed is 2.0 rad/s, the angular momentum of the body (in kg -

m^{2}

/s) is

A. 2.0

B. 0.5

C. 1.5

D. 1.0

Answer : Option D
Explaination / Solution:

$\begin{aligned} I = m k^{2} \\ m = 2 K g \\ k = 0.5 m \\ I = 2 \times 0.5 \times 0.5 = 0.5 K g m^{2} \end{aligned}$

angular momentum

$\begin{aligned} L = I ω \\ ω = 2 r a d / s \\ L = 0.5 \times 2 = 1.0 K g m^{2} / s \end{aligned}$

# System of Particles and Rotational Motion # CBSE 11TH PHYSICS Prepare / Learn

Q9.

The moment of inertia of a solid sphere about a diameter is 8000 gms $c m^{2}$ (mass of sphere = 50 gm, radius = 20 cm). The moment of inertia about a tangent will be

A. 8400 gm

c m^{2}

B. 280 gm

c m^{2}

C. 2.8

\times

1 0^{3}

c m^{2}

D. 2.8

\times

1 0^{3}

c m^{2}

Answer : Option D
Explaination / Solution:

I = 2/5 MR2 = 8000 gm cm2 , using parallel axis theorem the moment of Inertia about tangent to sphere is = 2/5 MR2+ MR2 = 7/5 MR2. =2.8 $\times$ $1 0^{4}$ gm cm2

$c m^{2}$

# System of Particles and Rotational Motion # CBSE 11TH PHYSICS Prepare / Learn

Q10. A particle moves with a constant velocity parallel to the x - axis. Its angular momentum with respect to the origin

A. is zero

B. goes on increasing

C. goes on decreasing

D. remains constant

Answer : Option D
Explaination / Solution:

As angular momentum is

\vec{L} = \vec{p} \times \vec{r} = m v r s i n θ

, Now rsinθ=perpendicular distance from x axis which is constant, so angular momentum is remains constant.

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