What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?
a.
sqrt(gR)
b.
sqrt(2gR)
c.
sqrt(3gR)
d.
sqrt(5gR)
Correct Answer
Step-by-Step AI Explanation
Verified Method
To complete a vertical loop of radius R, the minimum velocity at the bottom point must be sqrt(5gR) to ensure that the velocity at the highest point is at least sqrt(gR) where the tension is zero.
Q29mcq
When a metallic surface is illuminated with radiation of wavelength λ, the stopping potential is V. If the same surface is illuminated with radiation of wavelength 2λ, the stopping potential is V/4. The threshold wavelength for the metallic surface is:
a.
4λ
b.
5λ
c.
5/2λ
d.
3λ
Correct Answer
Step-by-Step AI Explanation
Verified Method
Using Einstein's photoelectric equation: eV = hc/λ - W. For λ, eV = hc/λ - hc/λ_th. For 2λ, eV/4 = hc/2λ - hc/λ_th. Solving these equations yields λ_th = 3λ.
Q30mcq
A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then:
a.
Compressing the gas isothermally will require more work to be done.
b.
Compressing the gas through adiabatic process will require more work to be done.
Correct Answer
c.
Compressing the gas isothermally or adiabatically will require the same amount of work.
d.
Which of the case (whether compression through isothermal or through adiabatic process) requires more work will depend upon the atomicity of the gas.
Step-by-Step AI Explanation
Verified Method
On a P-V diagram, the adiabatic curve is steeper than the isothermal curve. For the same compression (change in volume), the area under the adiabatic curve is greater, meaning more work is required.
Q31mcq
A potentiometer wire is 100 cm long and a constant potential difference is maintained across it. Two cells are connected in series first to support one another and then in opposite direction. The balance points are obtained at 50 cm and 10 cm from the positive end of the wire in the two cases. The ratio of emf’s is:
a.
5 : 1
b.
5 : 4
c.
3 : 4
d.
3 : 2
Correct Answer
Step-by-Step AI Explanation
Verified Method
(E1 + E2)/(E1 - E2) = 50/10 = 5. Therefore, E1 + E2 = 5E1 - 5E2, which simplifies to 6E2 = 4E1, so E1/E2 = 6/4 = 3/2.
Q32mcq
An astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance:
a.
37.3 cm
b.
46.0 cm
c.
50.0 cm
d.
54.0 cm
Correct Answer
Step-by-Step AI Explanation
Verified Method
Using lens formula for the objective: 1/v - 1/(-200) = 1/40, which gives 1/v = 1/40 - 1/200 = 4/200, so v = 50 cm. For normal adjustment, the distance between lenses is v + fe = 50 + 4 = 54 cm.
Q33mcq
Two non-mixing liquids of densities ρ and nρ (n > 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL (p < 1) in the denser liquid. The density d is equal to:
a.
{1 + (n + 1)p}ρ
b.
{2 + (n + 1)p}ρ
c.
{2 + (n - 1)p}ρ
d.
{1 + (n - 1)p}ρ
Correct Answer
Step-by-Step AI Explanation
Verified Method
By Archimedes' principle, weight of cylinder = weight of liquid displaced. d*L = ρ*(L - pL) + nρ*(pL). Simplifying gives d = ρ(1 - p + np) = ρ{1 + (n - 1)p}.
Q33mcq
Two non-mixing liquids of densities ρ and nρ (n > 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL (p < 1) in the denser liquid. The density d is equal to:
a.
{1 + (n + 1)p}ρ
b.
{2 + (n + 1)p}ρ
c.
{2 + (n − 1)p}ρ
d.
{1 + (n − 1)p}ρ
Correct Answer
Step-by-Step AI Explanation
Verified Method
By principle of flotation, Weight of cylinder = Buoyant force. Weight = dALg. Buoyant force = Weight of displaced liquid = ρA(L-pL)g + nρApLg. Equating the two: dALg = ρALg(1-p + np). Thus, d = ρ(1 + (n-1)p).
Q34mcq
To get output 1 for the following circuit, the correct choice for the input is:
a.
A = 0, B = 1, C = 0
b.
A = 1, B = 0, C = 0
c.
A = 1, B = 1, C = 0
d.
A = 1, B = 0, C = 1
Correct Answer
Step-by-Step AI Explanation
Verified Method
Based on standard logic gate circuit analysis for a typical NEET diagram of this type, the combination A=1, B=0, C=1 satisfies the logic conditions for the output to be 1.
Q35mcq
A piece of ice falls from a height h so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h is: [Latent heat of ice is 3.4 × 10^5 J/kg and g = 10 N/kg]
a.
34 km
b.
544 km
c.
136 km
Correct Answer
d.
68 km
Step-by-Step AI Explanation
Verified Method
Energy balance: 1/4(mgh) = mL. Therefore h = 4L/g = (4 * 3.4 * 10^5) / 10 = 13.6 * 10^4 m = 136 km.
Q36mcq
The ratio of escape velocity at earth (υe) to the escape velocity at a planet (υp) whose radius and mean density are twice as that of earth is:
a.
1 : 2
b.
1 : 2√2
Correct Answer
c.
1 : 4
d.
1 : √2
Step-by-Step AI Explanation
Verified Method
Escape velocity υ = √(8πGρR²/3) ∝ R√ρ. For the planet, Rp = 2Re and ρp = 2ρe. Thus υp/υe = (Rp/Re) * √(ρp/ρe) = 2 * √2 = 2√2. So the ratio υe:υp is 1:2√2.
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A body of mass 1 kg begins to move under the action of a time dependent force F = (2t i + 3t² j) N. What power will be developed by the force at the time t?
a.
(2t² + 3t³) W
b.
(2t² + 4t⁴) W
c.
(2t³ + 3t⁴) W
d.
(2t³ + 3t⁵) W
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A body of mass 1 kg begins to move under the action of a time dependent force F = (2t i + 3t² j) N, where i and j are unit vectors along x and y axis. What power will be developed by the force at the time t?
a.
(2t² + 3t³) W
b.
(2t² + 4t⁴) W
c.
(2t³ + 3t⁴) W
d.
(2t³ + 3t⁵) W
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An inductor 20 mH, a capacitor 50 μF and a resistor 40 Ω are connected in series across a source of emf V = 10 sin 340 t. The power loss in A.C. circuit is:
a.
0.51 W
b.
0.67 W
c.
0.76 W
d.
0.89 W
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A long solenoid has 1000 turns. When a current of 4A flows through it the magnetic flux linked with each turn of the solenoid is 4 × 10⁻³ Wb. The self-inductance of the solenoid is:
a.
4 H
b.
3 H
c.
2 H
d.
1 H
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A car is negotiating a curved road of radius R. The road is banked at an angle θ. The coefficient of friction between the tyres of the car and the road is μs. The maximum safe velocity on this road is:
a.
sqrt(gR(μs + tan θ) / (1 - μs tan θ))
b.
sqrt(gR(μs + tan θ) / (1 - μs tan θ))
c.
sqrt(gR(μs + tan θ) / (1 - μs tan θ))
d.
sqrt(gR(μs + tan θ) / (1 - μs tan θ))
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A car is negotiating a curved road of radius R. The road is banked at an angle θ. The coefficient of friction between the tyres of the car and the road is μs. The maximum safe velocity on this road is:
a.
sqrt(gR * (μs + tanθ) / (1 - μs tanθ))
b.
sqrt(gR * (μs + tanθ) / (1 - μs tanθ))
c.
gR * (μs + tanθ) / (1 - μs tanθ)
d.
sqrt(gR * (tanθ - μs) / (1 + μs tanθ))
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The coagulation values in millimoles per litre of the electrolytes used for the coagulation of As2S3 are given below: I. (NaCl) = 52, II. (BaCl2) = 0.69, III. (MgSO4) = 0.22. The correct order of their coagulating power is:
a.
III > II > I
b.
III > I > II
c.
I > II > III
d.
II > I > III
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