Average velocity of a particle executing SHM in one complete vibration is:
a.
A²/2ω
b.
zero
Correct Answer
c.
Aω/2
d.
Aω
Step-by-Step AI Explanation
Verified Method
Average velocity is defined as total displacement divided by total time. Since the particle returns to its starting position after one complete vibration, total displacement is zero.
Q92mcq
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 glycerin (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.
2 : 3
b.
3 : 4
c.
2 : 1
d.
1 : 2
Correct Answer
Step-by-Step AI Explanation
Verified Method
F1 = f/2. When a lens of liquid (glycerin) is inserted between them, it acts like a concave lens. The net power becomes zero or calculated via the combination formula, resulting in F1:F2 = 1:2.
Q93mcq
A particle moving with velocity V is acted by three forces shown by the vector triangle PQR. The velocity of the particle will:
a.
remain constant
Correct Answer
b.
change according to the smallest force
c.
increase
d.
decrease
Step-by-Step AI Explanation
Verified Method
A vector triangle formed by three forces indicates that their vector sum (net force) is zero. According to Newton's first law, if the net force is zero, the object's velocity remains constant.
Q94mcq
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 rH : rα will be:
a.
4 : 1
b.
1 : 4
c.
2 : 1
Correct Answer
d.
1 : 2
Step-by-Step AI Explanation
Verified Method
The radius of a charged particle path in a magnetic field is r = mv/qB = p/qB. Since p and B are same, r ∝ 1/q. For H+ (q=e) and α-particle (q=2e), rH/rα = (2e)/(e) = 2/1.
Q94mcq
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 rH : rα will be :
a.
4 : 1
b.
1 : 4
c.
2 : 1
Correct Answer
d.
1 : 2
Step-by-Step AI Explanation
Verified Method
The radius of the path is given by r = p/(qB). Since momentum p and field B are constant, r is inversely proportional to charge q. For H+ (q=e) and alpha particle (q=2e), the ratio rH/ra = qa/qH = 2e/e = 2:1.
Q95mcq
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.
4/9
b.
5/9
c.
1/9
d.
8/9
Correct Answer
Step-by-Step AI Explanation
Verified Method
Using elastic collision formulas: Final velocity v_A = [(m1-m2)/(m1+m2)]u = [(4m-2m)/(4m+2m)]u = (2m/6m)u = u/3. Energy lost = Initial KE - Final KE. Fraction lost = (1/2 m1 u^2 - 1/2 m1 v_A^2) / (1/2 m1 u^2) = 1 - (v_A/u)^2 = 1 - (1/3)^2 = 1 - 1/9 = 8/9.
Q95mcq
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.
4/9
b.
5/9
c.
1/9
d.
8/9
Correct Answer
Step-by-Step AI Explanation
Verified Method
For an elastic collision, the final velocity of body A (m1=4m) after colliding with body B (m2=2m) at rest is v = [(m1-m2)/(m1+m2)]u = [(4m-2m)/(4m+2m)]u = u/3. The fraction of energy lost is (1/2*m1*u^2 - 1/2*m1*v^2) / (1/2*m1*u^2) = (u^2 - (u/3)^2)/u^2 = 1 - 1/9 = 8/9.
Q96mcq
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.
60º west
b.
45º west
c.
30º west
Correct Answer
d.
0º
Step-by-Step AI Explanation
Verified Method
To cross the river along the shortest path (perpendicular to flow), the component of the swimmer's velocity opposing the river velocity must equal the river's speed. v*sin(theta) = vr. 20 * sin(theta) = 10, so sin(theta) = 0.5, theta = 30 degrees.
Q97mcq
In the circuits shown below, the readings of the voltmeters and the ammeters will be :
a.
V1 = V2 and i1 = i2
Correct Answer
b.
V2 > V1 and i1 > i2
c.
V2 > V1 and i1 = i2
d.
V1 = V2 and i1 > i2
Step-by-Step AI Explanation
Verified Method
Assuming ideal voltmeter (infinite resistance), in both circuits, the voltage drop across the resistor is 10V. Thus, V1 = V2 = 10V and I = V/R = 10/10 = 1A. Both circuits yield identical readings.
Q98mcq
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 90º around any of its coplanar axis in 0.1 s, the emf induced in the coil will be :
a.
2 × 10^-3 V
b.
0.02 V
Correct Answer
c.
2 V
d.
0.2 V
Step-by-Step AI Explanation
Verified Method
Initial flux = BAN. Final flux = 0 (since rotated 90 deg). EMF = Change in Flux / Time = (BAN)/t = (800 * 0.05 * 5e-5) / 0.1 = 0.02 V.
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At a point A on the earth’s surface the angle of dip, δ = +25º. At a point B on the earth’s surface the angle of dip, δ = -25º. We can interpret that :
a.
A is located in the northern hemisphere and B is located in the southern hemisphere
b.
A and B are both located in the southern hemisphere
c.
A and B are both located in the northern hemisphere
d.
A is located in the southern hemisphere and B is located in the northern hemisphere
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The displacement of a particle executing simple harmonic motion is given by y = A0 + A sin(ωt) + B cos(ωt). Then the amplitude of its oscillation is given by :
a.
sqrt(A0^2 + (A+B)^2)
b.
A + B
c.
A0 + sqrt(A^2 + B^2)
d.
sqrt(A^2 + B^2)
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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.
10%
c.
(13/3)%
d.
16%
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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.
25 J
b.
20 J
c.
30 J
d.
5 J
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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 / (πε0R)
b.
λ / (2πε0R)
c.
zero
d.
λ / (2πε0R^2)
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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.
10 rad/s
b.
10 pi rad/s
c.
10/pi rad/s
d.
sqrt(10)/pi rad/s
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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.
10 rad/s
b.
10 π rad/s
c.
10rad/s
d.
10/2π rad/s
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A small hole of area of cross-section 2 mm^2 is present near the bottom of a fully filled open tank of height 2 m. Taking g = 10 m/s^2, the rate of flow of water through the open hole would be nearly :
a.
2.23 x 10^-6 m^3/s
b.
6.4 x 10^-6 m^3/s
c.
12.6 x 10^-6 m^3/s
d.
8.9 x 10^-6 m^3/s
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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.
3:1
b.
sqrt(3):1
c.
2:1
d.
1:2
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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.
Plot with linear increase up to R and hyperbolic decrease after R
b.
Plot with jump at R
c.
Plot with constant inside and zero outside
d.
Plot with constant everywhere
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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 at a point Z0 below the free surface of water in a container. Taking g = 10 m/s^2, density of water = 10^3 kg/m^3, the value of Z0 is :
a.
1 cm
b.
0.5 cm
c.
100 cm
d.
10 cm
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Two particles A and B are moving in uniform circular motion in concentric circles of radii rA and rB with speed vA and vB respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be :
a.
rB : rA
b.
1 : 1
c.
rA : rB
d.
vA : vB
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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.
60 μA, zero
b.
zero, zero
c.
zero, 60 μA
d.
60 μA, 60 μA
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A parallel plate capacitor of capacitance 20 uF 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.
60 uA, zero
b.
zero, zero
c.
zero, 60 uA
d.
60 uA, 60 uA
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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(π/2 t)
b.
y(t) = 3 cos(π/2 t)
c.
y(t) = -3 cos 2πt
d.
y(t) = 4 sin(π/2 t)
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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(3*pi/2 * t)
b.
y(t) = 3 cos(pi/2 * t)
c.
y(t) = -3 cos(2*pi * t)
d.
y(t) = 4 sin(pi/2 * t)
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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.
1 : 2
b.
2 : 1
c.
4 : 9
d.
9 : 4
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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? (μwater = 4/3)
a.
0.05°
b.
0.1°
c.
0.266°
d.
0.15°
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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.
equal to angle of incidence
b.
90°
c.
180°
d.
0°
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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 the angle of refraction?
a.
Equal to angle of incidence
b.
90°
c.
180°
d.
0°
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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.
1/2 MgL
c.
Mgl
d.
MgL
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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.
1/2 MgL
c.
Mgl
d.
MgL
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Two point charges A and B, having charges +Q and –Q respectively, are placed at 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.
16F/9
b.
4F/3
c.
F
d.
9F/16
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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 (αCu = 1.7 × 10^-5 K^-1 and αAl = 2.2 × 10^-5 K^-1)
a.
88 cm
b.
68 cm
c.
6.8 cm
d.
113.9 cm
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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 attractive forces are dominant
b.
Z < 1 and repulsive forces are dominant
c.
Z > 1 and attractive forces are dominant
d.
Z > 1 and repulsive forces are dominant
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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.
C3A4
b.
C4A3
c.
C2A3
d.
C3A2
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