Test: Physics - 5 - MCAT MCQ

Acceleration due to gravity at Earth is expressed as
g = GM / R² ------------- (1)
Since we have to find the dimensional formula for the ratio between g and G, equation 1 can be written as
g / G = M / R² ------------- (2)
Thus, dimensional formula of g/G can be found by calculating the dimensional formula for M / R².
Since, dimensional formula of M is M and R is L hence, equation 2 can be written as
g / G = M / L²
Or g / G = ML^-2
Thus, C is the correct answer option.

If the net force acting on a body is zero then it means that theresultant of all the forces acting on the body is zero. Balanced forces produce zero net force acting on a body. Thus, if a body is acted upon by a balanced force, then net force acting on it is zero and hence, it will continue to retain its initial motion. Unbalanced forces have some non-zero value of force acting on a body and the body continues moving with non-uniform speedalong the unbalanced force. Acceleration is time rate of change of velocity. It can also be concluded from Newton’s first law that as the velocity is uniform, change in velocity is zero and so is the acceleration of the body. Thus in view of the above discussion statements, 1 and 2 are correct and 3isincorrect. Hence, D is the correct answer option.

Here we will apply the equation of rotational motion, which is given as
ωf = ω_i + 2αθ ------------ (1)
Putting the values in equation 1 we get
70 = ω_i + (2 x 5 x 2π) (π = 3.14)
70 = ω_i + 62.8
Or ωi = 7.2 rad/s
Therefore, C is the correct answer option.

Total energy of a body in SHM is given as
E = (1/2)kA² ------------- (1)
Initial energy is given by E¹ = (1/2)kA₁² ----------------- (2)
Final energy is given by E² = (1/2)kA₂² ---------------- (3)
Since A₂ = A₁ / 2, E² = (1/4)[(1/2)kA₁²] ---------------- (5)
Comparing equation 5 with 2 we get
E² : E² = 1 : 4
Therefore, D is the correct answer option.

Weight is given as
W = mg ---------------- (1)
Mass of the block can be given as
m = V ρ ------------- (2)
Volume of a cube is given as
V = (side)³ -------------- (3)
Therefore, putting the value in equation 3 we get
 = (0.1)3 Or V = 10^-3 m³
Putting the values of V and density in equation 2 we get
m = 0.99 kg
Putting the value of m and g in equation 1 we get
 = 9.7 N Therefore, A is the correct answer option.

Here, weight of the water drop is balanced by the electric force. Thus, we need to equate both kinds of forces to find the value of the electric field. Weight of the water drop is given as
W = mg ---------------- (1)
Putting the values in equation 1 we get
W = 10^-9 x 9.8
Or W = 9.8 x 10^-9 N
Electric force is given as F = qE -------------- (2)
Putting the values in equation 2 we get
F = 2.5 x 10^-20 x E ---------------- (3)
Putting the values in equation 2 we get
F = 2.5 x 10^-20 x E ---------------- (3)
Hence, B is the correct answer option.

If a charged particle enters a region of magnetic field, it experiences a force due to which the charged particles follow a curved path. The radius of the curved path is given as
r = (mv)/(qB) ------------- (1)
Putting the values in equation 1 we get
r = [(9.1 x 10^-31 x 10⁶) / (1.6 x 10^-19 x 0.01)]
r = 5.7 x 10^-4 m
Therefore, C is the correct answer option.

Energy of a photon is given as E = mc² -------------- (1)
Equation 1 can be written as E = (mc)c ----------------- (2)
Momentum of a photon is defined as the product of mass and velocity of the photon.
It is given as p = mc --------------- (3)
Using equation 3 in 2 we get E = pc --------------- (4)
Energy of the photon is given as 1 eV (1 eV = 1.6 x 10^-19 J).
As energy is given in eV, we need to convert it into Joules (as Joule is the SI unit of energy).
Putting the values in equation 4 we get p = 5.33 x 10^-28 kgms^-1
Hence, D is the correct answer option.

Here the initial speed, the final speed and the time taken are given and so we can use the kinematic equation
v = u + at ------------- (1)
Putting these values in equation 1 we get
27 = 15 + a x 45
Or a = 0.27 m/s²
Therefore, D is the correct answer option.

Frictional force develops due to the actual motion of a block on a surface. As the surface is rough, some frictional force will develop against the force of 100 N. Hence, D is an incorrect option. If the applied force is greater than the frictional force then only will the block of wood move. Hence, A is the correct answer option and B is an incorrect option. Also, if the frictional force is the same as the applied force, then the block of wood is at the verge of moving but it will show no physical motion. Therefore, C is an incorrect option. In view of the above discussion, E is an incorrect option.

Energy or work done is given as
E = Fd -------------- (1)
Putting the values in equation 1 we get
E = 70 x 30 Or E = 210 J
Therefore, C is the correct answer option.

A seismic wave originates at point A, travels along every direction and reaches point B. As it originates from A, it will reach point B after some timeandthis is thetime difference. Time difference can be given as
Time difference = distance / speed -------------- (1)
Distance between A and B is given as 2000 Km and speed of the seismic wave = 1.6 km/s. Therefore, putting these values in equation 1 we get
Time difference = 2000/1.6 seconds = 1250 seconds
1 s = 1 / 60 minutes
Therefore, A is the correct answer option.

Efficiency of a plant is given as
η = 1 - (T₂ / T₁) ------------ (1)
Putting the values in equation 1 we get
η = 1 - 600 / 1000
Or % η = 40%
Therefore, B is the correct answer option.

Let R₁ and R₂ be the resistances of the two wires connected in series and parallel respectively.
R_s = R₁ + R₂ = 50Ω; ------------ (1)
And, R_p = R₁ || R₂ = [(R₁ x R₂)/(R₁ + R₂)] = 80Ω --------------- (2)
From equation 1 R₂ = 50 - R₁ ----------- (3)
Putting equation 3 in 2 we get
[(R₁ x (50 - R₁)/(R₁ + (50 - R₁))] = 8
Or R₁ = 10Ω
Putting the value of R₁ in equation 3 we get
R₂ = 40Ω
Therefore, A is the correct answer option.

Light entering from one medium to another medium of a different refractive index bends and this bending is governed by Snell’s law. It is given as
μ₁ sin θ_i = μ₂ sin θ_r ---------------- (1)
Putting the values in equation 1 we get
1 * sin 30^o = 1.309 x sin θ_r
Or θ_r = sin^-1 (0.382)
Therefore, angle of refraction is sin^-1 (0.382). Whether a medium is denser or rarer is determined by the refractive index of the medium. Higher the refractive index, denser will be the medium. Since, refractive index of ice (1.309) is more than that of air (1), ice is denser than air.
Hence, C is the correct answer option.