CBSE 11TH PHYSICS - Online Test

Q1.

If there are n number of molecules per unit volume and m is the mass of each , $v_{x}$ is the x-component of velocity, pressure can be written as

A. P=mv2x¯¯¯¯¯

B. P=nmv2x¯¯¯¯¯

C. P=nv2x¯¯¯¯¯

D. P=2nmv2x¯¯¯¯¯

Answer : Option B
Explaination / Solution:

Pressure is due to collision of molecule with the wall of container.

Collision by moleculeto the wall of conntainer assumed to be perfectly elastic.

By the principle of conservation of momentum, the momentum imparted to the wall in the collision = 2mvx

the number of molecules hitting the wall in time $Δ t$ = $n A v_{x} Δ t$

n = no. of molecule per unit volume

A = Area of container

The total momentum transferred to the wall by these molecules in $Δ t$ time = $2 m v_{x} (n A v_{x} Δ t)$

Pressure P = F/A = rate of momentum transfer per unit area

$P = \frac{2 m v_{x} (n A v_{x} Δ t) / Δ t}{A} = n m {v^{2}}_{x}$

all molecules in a gas do not have the same velocity; there is a distribution in velocities. The above equation therefore, stands for pressure due to the group of molecules with speed vx in the x-direction and n stands for the number density of that group of molecules. The total pressurer due to all groups

$P = n m \bar{v_{x}^{2}}$

Thermal Properties of Matter Prepare / Learn

Q2. If V is the initial volume, ΔV the fractional change in volume of a substance for temperature change ΔT, the coefficient of volume expansion, αV is defined as

A. αV=(ΔVV)1ΔT

B. αV=(2VV)1T

C. αV=(VV)12T

D. αV=(V2V)1T

Answer : Option A
Explaination / Solution:

increase in volume per unit original volume per Kelvin rise in temperature is called coefficient of volume expansion, $α_{V}$

$α_{V} = (\frac{Δ V}{V}) \frac{1}{Δ T}$

Units and Measurements Prepare / Learn

Q3. If θ is the parallax angle of a planet at a distance 'D', when observed from two different positions on the Earth, separated by distance 'b', the expression for 'D' is

A. θb

\frac{b}{θ}

C. 2bθ

D. θ2b

Answer : Option B
Explaination / Solution:

Parallax Method of Measurement : Astronomers use an effect called parallax to measure distances to nearby stars. Parallax is the apparent displacement of an object because of a change in the observer's point of view.

To measure the distance D of a far away planet S by the parallax method, We observe it from two different positions (observatories) A and B on the Earth, separated by distance AB=b at the same time as shown in the given figure.

We measure the angle between the two directions along which the planet is viewed at these two points. The ∠ASB in the figure represented by symbol θ is called the parallax angle or parallactic angle.

As the planet is very far away, bD<<1 and therefore, θ is very small. Then we approximately take AB as an arc of length b of a circle with center at S and the distance D as the radius AS=BS so that AB=b=Dθ where θ is in radians.

Oscillations Prepare / Learn

Q4. The time period T of a spring system of mass m and spring constant k is given by

A. T=πkm−−√

B. T=mk−−√

T = 2 π \sqrt{\frac{k}{m}}

D. T=2πmk−−√

Answer : Option D
Explaination / Solution:

If the restoring force of a vibrating or oscillatory system is proportional to the displacement
of the body from its equilibrium position and is directed opposite to the direction of displacement,
the motion of the system is simple harmonic and it is given by
$x (t) = A c o s ω t$
where A, the maximum value of the displacement, is called the amplitude of the motion. If
T is the time for one complete oscillation, then
x(t + T) = x(t)

$A c o s ω (t + T) = A c o s ω t$
$ω T = 2 π$
or $T =$ $\frac{2 π}{ω}$
As angular frequency $ω$ is given by $ω = \sqrt{\frac{k}{m}}$ and $T = \frac{2 π}{ω}$

Then,time period of oscillation of mass m is given by

$T = 2 π \sqrt{\frac{m}{k}}$

Gravitation Prepare / Learn

Q5. The force of attraction due to a hollow spherical shell of uniform density, on a point mass situated inside it, is

A. positive

B. zero

C. negative

D. none of these

Answer : Option B
Explaination / Solution:

The gravitational force acting by a spherically symmetric shell upon a point mass inside it, is the vector sum of gravitational forces acted by each part of the shell, and this vector sum is equal to zero. That is, a mass m within a spherically symmetric shell of mass M will feel no net force

Motion in A Straight Line Prepare / Learn

Q6. Average speed is defined as the total path length travelled divided by the total time interval during which

A. the motion has taken place

B. uniform motion has taken place

C. maximum motion has taken place

D. minimum motion has taken placeminimum motion has taken place

Answer : Option A
Explaination / Solution:

Average speed is the ratio of distance traveled to time spent. To find average speed, divide the total number of km traveled by the total elapsed time in hours. The answer is the average speed in km per hour.

Waves Prepare / Learn

Q7. If y(x, t) = a sin (kx + ωt + φ) represents a wave function

A. travelling in the +ve x direction

B. travelling in the -ve x direction

C. direction of travel is sometimes –ve x and +x at other times

D. the equation does not tell the direction

Answer : Option B
Explaination / Solution:

On comparing above equation with y(x, t) = a sin (-kx + ωt + φ), we get Distance traveled by wave is along - x axis Hence y(x, t) = a sin (kx + ωt + φ) represents a wave function travelling in the -ve x direction

Work Energy and Power Prepare / Learn

Q8. work-energy theorem does not give information on

A. work done

B. difference of kinetic energies

C. change in kinetic energy

D. time dependence

Answer : Option D
Explaination / Solution:

According to work energy theorem : Net work done on a body equals change in its kinetic energy So it does not give any information about time dependence.

System of Particles and Rotational Motion Prepare / Learn

Q9. The moment of inertia of a body about any axis is

A. equal to the average of the moments of inertia of the body about a parallel axis passing through its centre of mass and the product of its mass and the square of the distance between the two parallel axes.

B. equal to the sum of the moment of inertia of the body about any axis passing through its centre of mass and the product of its mass and the square of the distance between the two parallel axes.

C. equal to the difference of the moment of inertia of the body about a parallel axis passing through its centre of mass and the product of its mass and the square of the distance between the two parallel axes.

D. equal to the sum of the moment of inertia of the body about a parallel axis passing through its centre of mass and the product of its mass and the square of the distance between the two parallel axes.

Answer : Option D
Explaination / Solution:

according to parallel axis theorem the moment of inertia of a body about any axis is equal to the sum of the moment of inertia of the body about a parallel axis passing through its Centre of mass and the product of its mass and the square of the distance between the two parallel axes.

$I = I_{c m} + M a^{2}$

Motion in A Plane Prepare / Learn

Q10. We can define the difference of two vectors A and B as the

A. sum of two vectors A and B' such that B' is equal to B multiplied by -1

B. sum of two vectors A and B' such that B' is equal to B multiplied by -2

C. sum of two vectors A and B' such that B' is equal to B multiplied by 1

D. sum of two vectors A and B' such that B' is equal to B multiplied by 0

Answer : Option A
Explaination / Solution:

Vector subtraction is defined in the following way.

The difference of two vectors, A - B , is a vector C that is, C = A - B
The addition of two vector such that C = A + (-B). B has been taken in opposite direction.

Thus vector subtraction can be represented as a vector addition.

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