Test: Physics - 4 - MCAT MCQ

Angular momentum is given as
L = Iω ------------ (1)
SI unit for I is kgm².
Hence, dimensional formula of I becomes ML².
Angular velocity is given as
ω = v/ r SI unit of v is m/s and that of r is m.
Hence, SI unit of angular velocity becomes (m/s)/m Or 1/s
Therefore, dimensional formula of angular velocity is T^-1 .
Thus, dimensional formula of angular momentum from equation 1 becomes
ML² / T Or ML²T^-1

Hence, D is the correct answer option.

As the water gallon is resting on the floor, normal reaction will be balanced by the weight of the gallon itself. Therefore,
Normal reaction = Weight of the gallon ------------- (1)
Weight of the gallon is given as F = mg------------- (2)
Putting the values in equation 1 we get
F = 500 x 9.8
Or F = 4900 N Using equation 1 we get
Normal reaction = 4900 N
Therefore, B is the correct answer option.

Here we will apply theequation of rotational motion, which is given as
θ = ωit + (1/2)αt² -------------- (1)
Putting the values in equation 1 we get
200 = 0 x t + (1/2) α5²
α = 400/25
Or α = 16 rad/s²
Therefore, E is the correct answer option.

Time period is given as
T = 2π √m / k -------------- (1)
Putting the values in equation 1 we get T = 2π √0.3 / 20
Or, T = 2 x 3.14 x 0.12 (π = 3.14)
T = 0.75 s
Therefore, C is the correct answer option.

Density is given as
ρ = m/V ------------- (1)
Volume of the body is given as
V = 0.7 x 0.1 x 0.08
Or V = 5.6 x 10^-3m³
Putting the values in equation 1 we get
ρ = 2 / 5.6 x 10^-3
Or ρ = 357.14 kg/m³
Specific gravity is given as
SG = ρ_body / ρ_water ---------------- (2)
Putting the values in equation 2 we get
SG = 357.14 / 1000
Or SG = 0.357
Therefore, A is the correct answer option.

Electrostatic force in a region is given as
F = [(1 / 4πε_o) (q₁q₂ / R)] -------------- (1)
Standard v alue of 1 / 4πε_o is 9 x 10⁹ Nm²C^-2
We are given values of charges in nC so we need to convert them into C.
1 nC = 10^-9C or -4 nC = - 4x10^-9 C
Putting the values in equation 1 we get
F = 9 x 10⁹ x [(4 x 10^-9 x 4 x 10^-9) / 0.22]
Or F = -3.6 x 10^-6 N
As force is negative, that suggests nature of force is attractive.
Hence, A is the correct answer option.

Magnetic field at the center of a solenoid is given as
B = (μ_onI) / l ------------- (1)
As length is given in cm we need to convert it into m.
1 cm = 10^-2 m 60 cm = 0.6 m
Putting the values in equation 1 we get
B = [(4π x 10^-7 x 400 x 3) / 0.6] (π = 3.14 )
B = 2.5 x 10^-3 T
Hence, A is the correct answer option.

Energy possessed by a photon is given as
E = hv --------------- (1)
Frequency is given in GHz so,
e need to convert it into Hz.
1 GHz = 109Hz 350 GHz = 3.5 x 10¹¹ Hz
Putting the values in equation 1 we get
E = 6.6 x 10^-34 x 3.5 * 1011
Or E = 2.31 x 10^-22 J
We need to convert energy in Joules into eV as given below
1.6 x 10^-19 J = 1 eV
1 J = 1 / (1.6 x 10^-19) eV
Or 2.31 x 10^-22 J = 1.44 x 10^-3 eV
Therefore, a photon with frequency of 350 GHz has energy of 1.44 x 10^-3 eV. Hence, C is the correct answer option.

Instantaneous speed of a body is the speed possessed by it at any particular time instant. Instantaneous speed is a variable and changes accordingly. Speedometer is a device that is used by the vehicles to know the speed possessed by it at that instant. Average velocity or speed provides speed of the body for the full journey. It is given as the total distance travelled in total time taken. As in the question the total time and the total distance are given, hence average speed can be found as
Average speed = Total Distance / Total Time ------------- (1)
Since, distance and time are given in kilometers and minutes we need to convert them Putting the values in equation 1 we get
Average speed = 8.33 m/s
Instantaneous acceleration is related to instantaneous speed. Hence, instantaneous acceleration cannot be found here. Thus, B is the correct answer option.

According toNewton’s second law of motion, force is time rate of change of momentum and is given as
F = p / t ------------ (1)
Momentum is given as
p = mv ------------- (2)
Putting the value of m and v in equation 2 we get
p = 45 x 2
Or p = 90 kgm/s
Putting the values of p and t in equation 1 we get
F = 90 N
Therefore, D is the correct answer option.

Efficiency of a motor is given as
% η = {P_output / P_input] x 100 -------------- (1)
Putting the values in equation 1, we get
% η = [100 / 500] * 100
Or, % η = 20%
Hence, C is the correct answer option.

This question can be solved by applying Doppler’s effect for sound waves. Doppler’s effect is related to change in original frequency of sound if either the source or the observer is moving simultaneously. Doppler’s effect is given as
f = [(v - v_r) / (v - v_s]f_o -------------- (1)
Putting the values in equation 1 we get
f = [(340) / (340 - 10] x 300
f = (34/33) x 300
Or f = 309.09 Hz
Therefore, E is the correct answer option.

Efficiency of a heat engine is given as
η = W / Q --------------- (1)
Putting the values in equation 1 we get
%η = 10000 / 12000 %
η = 0.833 x 100% Or %
η = 83.3 %
​​​​​​​Therefore, A is the correct answer option.

Current density is given as
J = σE -------------- (1)
Electric field is given as
E = V / l --------------- (2)
Putting the values in equation 2 we get
E = 200/1
Or E = 200 v/m
Putting the values in equation 1 we get
J = 1.45 x 10⁶ x 200
Or J = 2.9 x 10⁸ Am²
Hence, A is the correct answer option.

For a ray of light incident on a medium to not emerge from it is known as limiting case of total internal reflection. For the minimum angle the refracted ray travels along the interface. For the incident ray making an angle more than the minimum angle the ray will reflect back and this is known as total internal reflection. From Snell’s law we have
μ₁ sin θ_i = μ₂ sin θ_r ---------------- (1)
Putting the values in equation 1 we get
1.7 sin θ_i = 1.5 x sin 90^o
θ_i = sin^-1 (0.88)
Therefore, A is the correct answer option.