Test: Physics - 3 - MCAT MCQ

From dimensional analysis we know that dimensional formula of the left hand side of an expression should be the same as the dimensional formula of the individual quantities on the right hand side. Since, SI unit of acceleration is m/s². Therefore, dimensional formula of acceleration becomes LT^-2. SI unit of time is s. Therefore, its dimensional formula is T. As said earlier, d/t should have the same dimensional formula as a. Let dimensional formula of d be X. Hence, it can be written as
LT^-2 = X/T
LT^-1 = X
Hence, dimensional formula for d is LT^-1.
Thus, A is the correct answer option.

As the whole system is in static equilibrium, there will be no motion in the blocks. In other words,
weight of both the iron blocks should be the same.
Therefore,
Weight of A = Weight of B -------------- (1)
Weight of A = 200 N --------------- (2)
Using 2 in 1 we get
Weight of B = 200 N ------------- (3)
Weight of a body is given as
W = mg -------------- (4)
Putting the values in equation 4 we get
200 = m x 98 Or m = 20.41 kg
Therefore, A is the correct answer option.

Velocity with which the ferry-wheel is rotating is its angular velocity. It is given as
ω = [(N x 2π)/ t] ----------------- (1)
Putting the values in equation 1 we get
ω = [(100 x 2π)/ 15] (π = 3.14)
ω = 41.87 rad/s
Therefore, A is the correct answer option.

A body in SHM moves under a restoring force. The restoring force is always directed towards the equilibrium position. Displacement of a body in SHM is measured as the difference between the final position and the position of equilibrium. Amplitude in SHM is the maximum displacement of the body from the position of equilibrium. In other words, it can be said that amplitude is the maximum displacement of the body on either sides of the equilibrium as the body is SHM will continue performing a to and fro motion. Therefore, A is the correct answer option. Time period or period is the time taken to complete one cycle of oscillation. Hence, C is an incorrect option. Wavelength is the distance between two consecutive maxima or minima of a wave. Therefore, B is an incorrect answer option. Frequency of a body is defined as the number of oscillations about the equilibrium position per second. Therefore, D is an incorrect option. The magnitude of velocity with which the body in SHM moves is known as its speed. Therefore, E is an incorrect option.

This question can be solved by using the formula of specific gravity. Specific gravity tells us whether a substance will float or sink down in a fluid. It is given as
SG = ρ_body / ρ_water ---------------- (1)
Putting the values in equation 1 we get
SG = 700/1000 Or SG = 0.7
Specific gravity provides the fraction of surface of an object inside the fluid. If the specific gravity is equal to 1, then the object will float with zero percent of the surface outside the fluid. If the specific gravity is more than 1, then the object will sink completely inside the fluid. Since, specific gravity here is 0.7, percentage of the wooden surface inside the level of water is %
SG = 0.7 x 100 Or %SG = 70%
Therefore, 70 % of the block is inside the water and 30 % of the block is outside the water.
Hence, E is the correct answer option.

Average drift velocity of an electron is given as
v_d = σE / ne -------------- (1)
Electric field is given as
E = v/l --------------- (2)
Putting the values in equation 2 we get
E = 150/2.5 Or E = 60 V/m
Putting the values in equation 1 we get
v_d = [(3.5 x 10⁷ x 60) / (2 x 10²⁵ * 1.6 x 10 ^-19)] Or,
v_d = (2.1 x 10⁹) / 3.2 x 10⁶ Or
v_d = 656.25 m.s
Therefore, C is the correct answer option.

Magnetic field at the center of a coil due to the current flowing in it is given as
B = (µ_o / 4 π)(2πnI / r) -------------- (1)
Putting the values in equation 1 we get
B = [(4 π x 10^-7) / 4 π] x [(2π x 10 x 1.5)/0.1] Or
B = 10^-7x [(2 x 3.14 x 10 x 1.5) / 0.1] (π = 3.14) Or,
B = 10^-7 * 942 Or,
B = 9.42 x 10 ^-5 T
Hence, C is the correct answer option.

Joule is the SI unit of energy. eV is also a unit of energy but for microscopic charged particles. One electron volt (eV)is defined as the energy possessed by an electron moving in a unit potential field. We know that energy of a charged particle in a potential field is given as
E = q V J ------------- (1)
For an electronin a potential field of 1 V,energy can be expressed by using equation 1 as
E = e V J ------------- (2)
Putting the value in equation 2 we get
1 ev = 1.6 x 10^-19 x 1 J Or
1 ev = 1.6 x 10^-19 J
Therefore, A is the correct answer option.

The graph given in the question is between velocity and time. Acceleration is time rate of change of velocity. Velocity is constant here. Therefore, change in velocity is zero and therefore, acceleration is zero. Thus, options, B, C and D are incorrect. Since, velocity is uniform here, the body cannot be at rest and so A is an incorrect option. Therefore, E is the correct answer option.

Resultant force is given as
R = √( F1² + F2² + 2F1F² cos θ) ------------ (1)
As both the forces are acting orthogonally, θ = 90o.
Modifying equation 1 we get
R = √( F1² + F2² + 2F1F² cos 90^o) Or
R = √( F1² + F2²) ------------- (2)
If we take F₁ = 6 N and F₂ = 8 N and putting the values in equation 2 we get
R = 10N
Putting the values as mentioned in options A, C, D and E, we get the value of the resultant force as 6.4 N, 9.43 N, 11.3 N and 7.07 N.
Thus, for only one combination i.e. 6 N and 8 N we have a resultant force of 10 N.
Hence, B is the correct answer option.

Potential energy is given as
PE = mgh ---------------- (1)
Putting the values in equation 1 we get
1000 = 5 x 9.8 x h
h = 20.4 m
Hence, A is the correct answer option.

Speed of the wave is given as
v = fλ --------------- (1)
As the frequency is given in MHz, we need to convert it into Hz.
1 MHz = 10⁶ Hz
Therefore, 400 MHz = 400 x 106 Hz
Putting the values in equation 1 we get
2.5 x 10⁸ = 400 x 10⁶ x λ
λ = 0.625 m
Therefore, wavelength of the FM signal is 0.625 m and thus, B is the correct answer option.

This question can be solved by
Q = mc ΔT ---------------- (1)
As mass is given in grams we need to convert it into kg.
1g = 10^-3 kg 20g = 0.02kg
Change in temperature is given as
ΔT = T₂ - T₁
Putting the values in equation 1 we get
740 = 0.02 x 1000 x (T₂ - 500) Or
T₂ = 537 K
Therefore, C is the correct answer option.

Force experienced by the beta particle is given as
F = qvB sin θ ---------------- (1)
As the beta particle is moving perpendicularly to the magnetic field, θ = 90^o. Charge onabeta particle is equal to the charge onanelectron;
Putting the values in equation 1 we get
F = 1.6 x 10^-19 x 10⁴ x 0.01 x sin 90^o
Or, F = 1.6 x 10^-17 x 1 N
Or, F = 1.6 x 10^-17
Hence, B is the correct answer option.

Refractive index of one medium with respect to another medium is given as
2μ¹ = μ²/ μ_¹
Here we have been given refractive index of diamond with respect to air = 2.4 i.e.
2.4 = μ_diamond /1 Or μ_diamond = 2.4
Also, refractive index of water with respect to air = 1.33 i.e.
1.33 = μ_water /1 Or μ_water = 1.33
Thus, refractive index of diamond with respect to water becomes
_diamondμ^water = 2.4 / 1.33
Or _diamondμ^water = 1.80
Thus, C is the correct answer option.