Test: Physics - 2 - 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. Force has the SI unit of kgms^-2 . Therefore, the dimensional formula of force becomes MLT^-2. Dimensional formula of x is L. Hence, dimensional formula of x^-1 becomes L^-1. As said earlier, Xx1 should have the same dimensional formula as F. Therefore, it can be written as MLT^-2 = X * L^-1
X = ML²T^-2
Therefore, E is the correct answer option.

Weight of a body is given as
W = mg -------------- (1)
Putting the value of W and g in equation 1 we get
1000 = m x 9.8 m
= 102.04 kg
Therefore, A is the correct answer option.

Time taken to complete one rotation is known as time period.
Angular velocity is related to time period as
ω = 2π/T ---------------- (1)
Putting the values of (π = 3.14) and ω in equation 1 we get
2.5 = (2 x 3.14)/T
T = 2.51 s
Therefore, B is the correct answer option.

Time period is given as
 = 2π √(M/k) ---------------- (1)
At the surface of the Moon, acceleration due to gravity is (1/6)^th of that on the surface of the Earth. As, there is no term related to acceleration due to gravity in equation 1, time period of the system will remain unaffected. Hence, time period of the system on the moon will be the same as that of the system on the Earth.
Therefore, C is the correct answer option.

Specific gravity is a dimensionless quantity and is given as
SG = ρ_fluid/ ρ_water ---------------- (1)
It is quite obvious from equation 1 that specific gravity is a unit less quantity.
Putting the values of densities in equation 1 we get
SG = 944 / 1000 Or SG = 0.944
herefore, C is the correct answer option.

Electric dipole moment between two charges of opposite polarity is given as
p = Qd ----------- (1)
The distance is in nm so we need to convert it into m. 1 nm = 10^-9 m
Putting the values in equation 1 we get
P = 1.6 × 10^-19 × 10^-9
Or, 1.6 × 10^-28 Cm
Hence, D is the correct answer option.

Magnetic field due toalong straight conductor is given as
B = [(μ₀/4π)(2I/a)] -------------- (1)
Putting the values in equation 1 we get
B = (4π × 10^-7 / 4π) x (2 x  2 / 0.05) B
= 8 × 10^-6 T
Hence, A is the correct answer option.

Threshold frequency is the minimum frequency required to eject photoelectrons out of a material in photoelectric effect.
It is given as Φ = hv_o -------------- (1)
Work function is given in eV.
So, we need to convert it into Joules.
1 eV = 1.6 x 10^-19 J
5.01 eV = 8.02 x 10^-19 J
Putting the values in equation 1 we get
8.02 x 10^-19 = 6.6 x 10-34 x v_o
v_o = 1.21 × 10¹⁵ Hz
Therefore, A is the correct answer option.

The graph given in the question is between velocity and time. Slope of the velocity time graph is linear here. Therefore, velocity increases with each instant but change in velocity per unit time is constant throughout the travel. Thus, 3 is an incorrect statement and so is option C. Acceleration of a body is defined as the rate of change of velocity per unit time. As said earlier, for a linear slope between velocity and time, change in velocity is constant per unit time and thus, acceleration is constant for the entire travel. Therefore, statement 1 isincorrect and so is option B. A body falls freely under gravity only. A free falling body always experiences uniform acceleration throughout the travel. Thus, we can say that acceleration is constant for a free fall and the graph essentially represents the motion of free fall. Thus, statement 2 is correct and so A is the correct answer option. In view of the above discussion, options D and E are incorrect as well.

A body undergoes acceleration due to an unbalanced force. The unbalanced force here is given as
F = 25 - 12 Or F = 13N
According to Newton’s second law of motion
F = ma -------------- (1)
13 = 1.5 x a
a = 8.67 m/s²
Therefore, E is the correct answer option.

Power is given as
P = W/t ---------------- (1)
Putting the values in equation 1 we get
P = 2000 / 25
P = 80 J/s or Watt
Hence, C is the correct answer option.

Thespeed of sound in solids like steel and iron is 5000 m/s and 5130 m/s.The speed of sound in liquidslike water at 0^o C and 20o C is 1402 m/s and 1482 m/srespectively. The speed of sound in air (gas)at 0o C and 20^o C is 331.5 m/s and 344 m/srespectively. Thus, from the above discussion it can be concluded that the speed of sound in solids is more than that in liquids and air. Therefore,thecorrect arrangementfor speeds of soundis air (gas) < liquids < solids. Thus, C is the correct answer option.

This question can be solved by applying Charles’s law, which is given as
V₁/ T₁ = V₂/ T₂ -------------- (1)
Putting the values in equation 1 we get
10/313 = V₂/373
V₂ = 11.92 m³
Therefore, A is the correct answer option.

Current flowing through the conductor is given as
I = neAv_d --------------- (1)
Putting the values in equation 1 we get
I = 6 × 10²⁴ 1.6 × 10^-19 × 2 × 10^-4 × 10^-3
I = 0.19A
Hence, E is the correct answer option.

The apparent depth is given as
_glassμ^air = μ_glass / μ^air = real depth/ apparent depth ---------------- (1)
Putting the values in equation 1 we get
1.5/1 = 15 cm / apparent depth
apparent depth = 10 cm
Hence, E is the correct answer option.