When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60° with horizontal, it can travel a distance x1 along the plane. But when the inclination is decreased to 30° and the same object is shot with the same velocity, it can travel x2 distance. Then x1 : x2 will be:
a.
1 : 2√3
b.
1 : 2
c.
2 : 1
d.
1 : √3
Correct Answer
Step-by-Step AI Explanation
Verified Method
The stopping distance s on an inclined plane is given by s = u²/2g sinθ. Thus, x1/x2 = sin(30°)/sin(60°) = (1/2) / (√3/2) = 1/√3.
Q92mcq
A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5 × 10⁻² N/m. The pressure inside the bubble equals the pressure at a point Z0 below the free surface of water in a container. Taking g = 10 m/s², density of water = 10³ kg/m³, the value of Z0 is:
a.
0.5 cm
b.
100 cm
c.
10 cm
d.
1 cm
Correct Answer
Step-by-Step AI Explanation
Verified Method
Excess pressure in a soap bubble is 4T/R. Equating this to gauge pressure ρgZ0: 4T/R = ρgZ0. Substituting values: (4 * 2.5 * 10⁻²) / (1 * 10⁻³) = 10³ * 10 * Z0, solving gives Z0 = 0.01 m = 1 cm.
Q93mcq
Two similar thin equi-convex lenses, of focal length f each, are kept coaxially in contact with each other such that the focal length of the combination is F1. When the space between the two lenses is filled with glycerine (which has the same refractive index (μ = 1.5) as that of glass) then the equivalent focal length is F2. The ratio F1 : F2 will be:
a.
3 : 4
b.
2 : 1
c.
1 : 2
Correct Answer
d.
2 : 3
Step-by-Step AI Explanation
Verified Method
Initial F1 = f/2. When glycerine is filled, the central part acts as a diverging lens with focal length -f. The combination power becomes P = 1/f + 1/f - 1/f = 1/f, so F2 = f. Ratio F1/F2 = (f/2)/f = 1/2.
Q94mcq
α-particle consists of:
a.
2 protons only
b.
2 protons and 2 neutrons only
Correct Answer
c.
2 electrons, 2 protons and 2 neutrons
d.
2 electrons and 4 protons only
Step-by-Step AI Explanation
Verified Method
An α-particle is a Helium nucleus (He²⁺), which consists of 2 protons and 2 neutrons.
Q95mcq
Which of the following acts as a circuit protection device?
a.
Fuse
Correct Answer
b.
Conductor
c.
Inductor
d.
Switch
Step-by-Step AI Explanation
Verified Method
A fuse is a safety device with a low melting point that melts and breaks the circuit when excess current flows, preventing damage.
Q96mcq
In total internal reflection when the angle of incidence is equal to the critical angle for the pair of media in contact, what will be angle of refraction?
a.
90°
Correct Answer
b.
180°
c.
0°
d.
Equal to angle of incidence
Step-by-Step AI Explanation
Verified Method
By definition, the critical angle is the angle of incidence for which the angle of refraction is 90°.
Q97mcq
The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path the angle at which he should make his strokes w.r.t. north is given by:
a.
45° west
b.
30° west
Correct Answer
c.
0°
d.
60° west
Step-by-Step AI Explanation
Verified Method
For shortest path, the swimmer must swim upstream at an angle θ such that the component of his velocity along the river cancels the river flow. sin(θ) = v_river / v_swimmer = 10 / 20 = 1/2. Thus θ = 30° west.
Q97mcq
The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by:
a.
45° west
b.
30° west
Correct Answer
c.
0°
d.
60° west
Step-by-Step AI Explanation
Verified Method
To cross the river along the shortest path (perpendicular to the bank), the net velocity must be perpendicular to the river flow. Using sine rule, sin(θ) = v_river / v_swimmer = 10 / 20 = 1/2. Thus, θ = 30° west of north.
Q98mcq
A parallel plate capacitor of capacitance 20 μF is being charged by a voltage source whose potential is changing at the rate of 3 V/s. The conduction current through the connecting wires, and the displacement current through the plates of the capacitor, would be, respectively:
a.
Zero, zero
b.
Zero, 60 μA
c.
60 μA, 60 μA
Correct Answer
d.
60 μA, zero
Step-by-Step AI Explanation
Verified Method
Conduction current ic = C * (dV/dt) = 20 × 10⁻⁶ * 3 = 60 μA. In a charging capacitor, the displacement current id is equal to the conduction current ic, so id = 60 μA.
Q98mcq
A parallel plate capacitor of capacitance 20 μF is being charged by a voltage source whose potential is changing at the rate of 3 V/s. The conduction current through the connecting wires, and the displacement current through the plates of the capacitor, would be, respectively:
a.
Zero, zero
b.
Zero, 60 μA
c.
60 μA, 60 μA
Correct Answer
d.
60 μA, zero
Step-by-Step AI Explanation
Verified Method
The conduction current i_c = C(dV/dt) = 20 × 10^-6 F × 3 V/s = 60 μA. In a charging capacitor, the displacement current i_d is equal to the conduction current i_c.
🎉 10 Free Sample Solutions Completed
Unlock All 62 Questions & Solutions
Sign up free in seconds to unlock step-by-step AI answers for the remaining 52 questions.
In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where X = (A^2 B^1/2) / (C^1/3 D^3) will be:
a.
10%
b.
3/13%
c.
16%
d.
– 10%
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Two parallel infinite line charges with linear charge densities +λ C/m and –λ C/m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges?
a.
λ / (πε_0 2R)
b.
Zero
c.
λ / (πε_0 2R^2)
d.
λ / (πε_0 R)
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The displacement of a particle executing simple harmonic motion is given by y = A_0 + A sin(ωt) + B cos(ωt). Then the amplitude of its oscillation is given by:
a.
A + B
b.
sqrt(A_0^2 + A^2 + B^2)
c.
sqrt(A^2 + B^2)
d.
sqrt(A_0^2 + (A + B)^2)
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
In a double slit experiment, when light of wavelength 400 nm was used, the angular width of the first minima formed on a screen placed 1 m away, was found to be 0.2°. What will be the angular width of the first minima, if the entire experimental apparatus is immersed in water? (μ_water = 4/3)
a.
0.1°
b.
0.266°
c.
0.15°
d.
0.05°
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
In a double slit experiment, when light of wavelength 400 nm was used, the angular width of the first minima formed on a screen placed 1 m away, was found to be 0.2°. What will be the angular width of the first minima, if the entire experimental apparatus is immersed in water? (μ_water = 4/3)
a.
0.1°
b.
0.266°
c.
0.15°
d.
0.05°
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Two particles A and B are moving in uniform circular motion in concentric circles of radii r_A and r_B with speed v_A and v_B respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be:
a.
1 : 1
b.
r_A : r_B
c.
v_A : v_B
d.
r_B : r_A
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A 800 turn coil of effective area 0.05 m^2 is kept perpendicular to a magnetic field 5 × 10^–5 T. When the plane of the coil is rotated by 90° around any of its coplanar axis in 0.1 s, the emf induced in the coil will be:
a.
0.02 V
b.
2 V
c.
0.2 V
d.
2 × 10^–3 V
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be (g = 10 m/s^2):
a.
10π rad/s
b.
10 rad/s
c.
10/(2π) rad/s
d.
10 rad/s
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L + l). The elastic potential energy stored in the extended wire is:
a.
1/2 MgL
b.
Mgl
c.
MgL
d.
1/2 Mgl
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A cylindrical conductor of radius R is carrying a constant current. The plot of the magnitude of the magnetic field B with the distance d from the centre of the conductor, is correctly represented by the figure:
a.
Graph showing B increasing linearly to R then staying constant
b.
Graph showing B increasing then falling to zero
c.
Graph showing B constant then increasing
d.
Graph showing B increasing linearly to R then falling hyperbolically
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Body A of mass 4m moving with speed u collides with another body B of mass 2m, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body A is :
a.
5/9
b.
1/9
c.
8/9
d.
4/9
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Body A of mass 4m moving with speed u collides with another body B of mass 2m, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body A is:
a.
5/9
b.
1/9
c.
8/9
d.
4/9
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is : (α_Cu = 1.7 × 10^-5 K^-1 and α_Al = 2.2 × 10^-5 K^-1)
a.
68 cm
b.
6.8 cm
c.
113.9 cm
d.
88 cm
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is: (α_Cu = 1.7 × 10^–5 K^–1 and α_Al = 2.2 × 10^–5 K^–1)
a.
68 cm
b.
6.8 cm
c.
113.9 cm
d.
88 cm
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the fig. y-projection of the radius vector of rotating particle P is:
a.
y(t) = 3 cos(pi * t / 2)
b.
y(t) = -3 cos(2 * pi * t)
c.
y(t) = 4 sin(pi * t / 2)
d.
y(t) = 3 cos(3 * t / 2)
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A force F = 20 + 10y acts on a particle in y-direction where F is in newton and y in meter. Work done by this force to move the particle from y = 0 to y = 1 m is
a.
20 J
b.
30 J
c.
5 J
d.
25 J
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Ionized hydrogen atoms and α-particles with same momenta enter perpendicular to a constant magnetic field, B. The ratio of their radii of their paths r_H : r_α will be:
a.
1 : 4
b.
2 : 1
c.
1 : 2
d.
4 : 1
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Two point charges A and B, having charges +Q and –Q respectively, are placed at a certain distance apart and force acting between them is F. If 25% charge of A is transferred to B, then force between the charges becomes:
a.
4F/3
b.
F
c.
9F/16
d.
16F/9
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Six similar bulbs are connected as shown in the figure with a DC source of emf E and zero internal resistance. The ratio of power consumption by the bulbs when (i) all are glowing and (ii) in the situation when two from section A and one from section B are glowing, will be:
a.
2 : 1
b.
4 : 9
c.
9 : 4
d.
1 : 2
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A small hole of area of cross-section 2 mm² is present near the bottom of a fully filled open tank of height 2 m. Taking g = 10 m/s², the rate of flow of water through the open hole would be nearly:
a.
6.4 × 10⁻⁶ m³/s
b.
12.6 × 10⁻⁶ m³/s
c.
8.9 × 10⁻⁶ m³/s
d.
2.23 × 10⁻⁶ m³/s
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
In the circuits shown below, the readings of voltmeters and the ammeters will be [Circuit 1: 10V source, 10 Ohm resistor, V1 voltmeter, A1 ammeter; Circuit 2: 10V source, 10 Ohm resistor, 10 Ohm resistor, V2 voltmeter, A2 ammeter]
a.
V2 > V1 and i1 > i2
b.
V2 > V1 and i1 = i2
c.
V1 = V2 and i1 > i2
d.
V1 = V2 and i1 = i2
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
In the circuits shown below, the readings of voltmeters and the ammeters will be (Circuit 1: Source 10V, Resistor 10Ω, Ammeter in series, Voltmeter in parallel across R; Circuit 2: Source 10V, Resistor 10Ω in series, Ammeter in series, Voltmeter in parallel across R):
a.
V2 > V1 and i1 > i2
b.
V2 > V1 and i1 = i2
c.
V1 = V2 and i1 > i2
d.
V1 = V2 and i1 = i2
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A compound is formed by cation C and anion A. The anions form hexagonal close packed (hcp) lattice and the cations occupy 75% of octahedral voids. The formula of the compound is :
a.
C4A3
b.
C2A3
c.
C3A2
d.
C3A4
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A gas at 350 K and 15 bar has molar volume 20 percent smaller than that for an ideal gas under the same conditions. The correct option about the gas and its compressibility factor (Z) is :
a.
Z < 1 and repulsive forces are dominant
b.
Z > 1 and attractive forces are dominant
c.
Z > 1 and repulsive forces are dominant
d.
Z < 1 and attractive forces are dominant
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A gas at 350 K and 15 bar has molar volume 20 percent smaller than that for an ideal gas under the same conditions. The correct option about the gas and its compressibility factor (Z) is :
a.
Z < 1 and repulsive forces are dominant
b.
Z > 1 and attractive forces are dominant
c.
Z > 1 and repulsive forces are dominant
d.
Z < 1 and attractive forces are dominant
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
