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Can you explain the answer of this question below:
An alternating e.m.f. of angular frequency ω is applied across an inductance. The instantaneous power developed in the circuit has an angular frequency
  • A: ω/4
  • B: ω/2
  • C: ω
  • D: 

The answer is d.

Divya Sara answered
The instantaneous values of emf and current in inductive circuit are given by E=E0sinωt and i=i0sin(ωt−π2)respectively. So, Pinst=Ei=E0sinωt*i0sin(ωt−π2) =E0i0sinωt(sinωtcosπ2−cosωtsinπ2) =E0i0sinωt cosωt =12E0i0sin2ωt (sin2ωt=2sinωt cosωt) Hence, angular frequency of instantaneous power is 2ω.

If a bullet of mass 5 gm moving with velocity 100 m/sec, penetrates the wooden block upto 6 cm. Then the average force imposed by the bullet on the block is
  • a)
    8300 N
  • b)
    417 N
  • c)
    830 N
  • d)
    Zero
Correct answer is option 'B'. Can you explain this answer?

Vijay Bansal answered
Here too we use equation of motion
v^2 = u^2 + 2as
2as = v^2 - u^2
2 x a x (6/100) = 0 - (100)^2
12a / 100 = - 10000
a = -1000000 / 12 m/s^2
This is the average retardation of the bullet
Avg force F = m a
= (5/1000) x 1000000 / 12 = 416.66 N
approx 417 newton

Infrared radiation is detected by
  • a)
    spectrometer
  • b)
    pyrometer
  • c)
    nanometer
  • d)
    photometer
Correct answer is option 'B'. Can you explain this answer?

Kaneez Fatima answered
A photometer is an instrument that measures light intensity or optical properties. ... A pyrometer is a type of remote-sensing thermometer used to measure the temperature of a surface. Infrared radiation can be detected by pyrometer.

Radius of the earth is 6400 km. The radius of the orbit of a stationary satellite is about
  • a)
    36000 km
  • b)
    29600 km
  • c)
    42400 km
  • d)
    infinity
Correct answer is option 'A'. Can you explain this answer?

Mumtaj Ali answered
For geostationary satellite,
Time period = 24 hrs, Height=35800km, Escape velocity= 3.1 km/s.These are called stationary satellite because such satellites appear stationary due to zero relative velocity w. r. t. earth.

A 2m long Aluminium pipe at 27 oC is heated until it is 2.0024m at 77 oC. The coefficient of linear expansion of aluminium is
  • a)
    24 x 10-6  oC-1
  • b)
    24 x 10-4  oC-1
  • c)
    25 x 10-6  oC-1
  • d)
    25 x 10-4  oC-1
Correct answer is option 'C'. Can you explain this answer?

Hansa Sharma answered
∆l= L c ∆T (here c is coefficient of linear expansion, ∆l is change in length, L is previous length and ∆T is change in temperature ) 0.0024 = 2 × c × 50c = 24× 10–6 °C
So (a) should be answer.

An ideal gas has a volume of V at 2 atm pressure. Keeping the temprature of gas constant, its pressure is doubled. The volume of gas will become
  • a)
    0.5 V
  • b)
    V
  • c)
    2 V
  • d)
    4 V
Correct answer is option 'A'. Can you explain this answer?

Suyash Jain answered
Explanation:
To solve this problem, we can use the ideal gas law, which states that the pressure (P), volume (V), and temperature (T) of an ideal gas are related by the equation PV = nRT, where n is the number of moles of gas and R is the ideal gas constant.

Given that the temperature of the gas is constant, we can rewrite the ideal gas law as P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

In this case, the initial pressure (P1) is 2 atm, and the final pressure (P2) is 4 atm (double the initial pressure). We want to find the final volume (V2).

Step 1:
Using the ideal gas law equation, we can write:
P1V1 = P2V2

Step 2:
Plugging in the given values, we have:
2 atm * V1 = 4 atm * V2

Step 3:
Simplifying the equation, we can cancel out the atm units:
2V1 = 4V2

Step 4:
Dividing both sides of the equation by 2, we get:
V1 = 2V2

Step 5:
Finally, rearranging the equation, we find:
V2 = 0.5V1

Therefore, the volume of the gas will become 0.5 times the initial volume. This means that the correct answer is option 'A' - 0.5V.

A cyclotron can not accelerate
  • a)
    protons
  • b)
    deuterons
  • c)
    α-particles
  • d)
    electrons
Correct answer is option 'D'. Can you explain this answer?

Jeeshan Ahmed answered
Cyclotron cannot be used to accelerate electrons because electrons are of very small mass. Thus, the velocity will be increased to such a great extent that the electron will be thrown out of the step with the oscillating field.

A thin uniform circular ring is rolling down an inclined plane of inclination 300 without slipping. Its linear acceleration along the inclined plane will be
  • a)
    g/2
  • b)
    g/3
  • c)
    g/4
  • d)
    2g/3
Correct answer is option 'C'. Can you explain this answer?

Rajeev Saxena answered
Acceleration on an inclined plane 
a= g sinθ/ (1 + I/MR^2)
for circular rings: I= MR^2
so by putting the value in above equation we get
a= g sinθ/ 2
a = g sin30/2
a= g/4

The work done increasing the size of a rectangular soap film with dimensions 8 cm x 3.75 cm to 10 cm x 6 cm is 2 x 10-4 J . The surface tension of the film in Nm -1 is
  • a)
    1.65 x 10-2
  • b)
    3.33 x 10-2
  • c)
    6.6 x 10-2
  • d)
    8.25 x 10-2
Correct answer is option 'B'. Can you explain this answer?

Sneha Datta answered
To solve this problem, we can use the formula for the work done in increasing the size of a soap film:

Work = Surface tension * Change in area

Let's break down the problem step by step:

Given information:
Dimensions of the initial soap film: 8 cm x 3.75 cm
Dimensions of the final soap film: 10 cm x 6 cm
Work done = 2 x 10^-4 J

Step 1: Calculating the change in area
To find the change in area, we subtract the initial area from the final area:

Initial area = 8 cm * 3.75 cm = 30 cm^2
Final area = 10 cm * 6 cm = 60 cm^2

Change in area = Final area - Initial area
Change in area = 60 cm^2 - 30 cm^2 = 30 cm^2

Step 2: Calculating the surface tension
We can rearrange the formula for work to solve for surface tension:

Surface tension = Work / Change in area

Surface tension = 2 x 10^-4 J / 30 cm^2

However, we need to convert the units of area from cm^2 to m^2 because the unit of surface tension is N/m^2 (Nm^-1).

1 m^2 = (100 cm)^2 = 10,000 cm^2

Surface tension = 2 x 10^-4 J / (30 cm^2 * (1 m^2 / 10,000 cm^2))
Surface tension = 2 x 10^-4 J / (30 * 10^-4 m^2)
Surface tension = 2 / 30 N/m^2
Surface tension = 1 / 15 N/m^2

Step 3: Converting the surface tension to scientific notation
To convert the surface tension to scientific notation, we divide the number by 10 until it is between 1 and 10. We count the number of divisions and use that as the exponent.

1 / 15 N/m^2 = 0.06667 N/m^2
Scientific notation = 6.667 x 10^-2 N/m^2

The given options are in scientific notation, so we can see that the surface tension matches option (b): 3.33 x 10^-2 N/m^2.

Therefore, the correct answer is option (b): 3.33 x 10^-2 N/m^2.

If liquid level falls in a capillary then radius of capillary will be
  • a)
    Increase
  • b)
    Decrease
  • c)
    Unchanged
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Rithika Singh answered
Explanation:

When a liquid rises or falls in a capillary tube, it is due to the interaction of the cohesive forces between the liquid molecules and the adhesive forces between the liquid and the walls of the capillary. The height to which the liquid rises or falls is inversely proportional to the diameter of the capillary tube.

When the liquid level falls in a capillary, it means that the adhesive forces between the liquid and the walls of the capillary are greater than the cohesive forces between the liquid molecules. This happens due to the presence of surface tension.

Surface tension is the force that holds the surface molecules of a liquid together, creating a sort of "skin" on the surface. When the liquid level falls, the surface tension causes the diameter of the capillary to decrease. This is because the surface tension acts to minimize the surface area of the liquid, and decreasing the diameter of the capillary reduces the surface area of the liquid in contact with the walls of the capillary.

Hence, the correct answer is option B - Decrease.

A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved
  • a)
    14 m/s
  • b)
    3 m/s
  • c)
    3.92 m/s
  • d)
    5 m/s
Correct answer is option 'A'. Can you explain this answer?

Pooja Mehta answered
Given,Length of String, l = 1.96 mMass of Ball, m = 0.25 KgMaximum Tension of String, Tmax = 25 NLet the speed of the ball is v m/sIn the horizontal circular motion of the ball tension in the string is balanced by the centrifugal force (mv2/l) and hence the maximum tension in the string will be for the maximum speed of the ball (since m and l are fixed).Therefore,Tmax=mv^2/l=> v^2=Tmax * l/m = 25 x 1.96/0.25=> v = 5 x 1.4/0.5 = 14 m/sTherefore, maximum speed of the ball will be 14 m/s.

Which of the following forms a perfect image free from all aberrations?
  • a)
    plane mirror
  • b)
    spherical lens
  • c)
    cylindrical lens
  • d)
    spherical mirror
Correct answer is option 'A'. Can you explain this answer?

Rajat Kapoor answered
Aberration, in optical systems, such as lenses and curved mirrors, the deviation of light rays through lenses, causing images of objects to be blurred. In an ideal system, every point on the object will focus to a point of zero size on the image. Practically, however, each image point occupies a volume of finite size and unsymmetrical shape, causing some blurring of the whole image. Unlike a plane mirror, which yields images free of aberrations, a lens is an imperfect image producer, becoming ideal only for rays passing through its centre parallel to the optical axis (a line through the centre, perpendicular to the lens surfaces). 

A beaker containing a liquid of density (ρ) moves up with an acceleration (a). The pressure due to liquid at a depth (h) below the surface of the liquid is
  • a)
    h ρ g
  • b)
    2h ρ g
  • c)
    hρ(g + a)
  • d)
    hρ(g - a)
Correct answer is option 'C'. Can you explain this answer?

Vijay Bansal answered
As the beaker is moving up with acceleration, so we have to consider pseudo force on the pressure element. 
Or simply in P = hpg , (p = density of liquid)
g will change to its apparent value g' = (g+a)
So, pressure at depth h will be, P= h p (g+a)

The resistance of a 10 m long wire is 10 Ω. Its length is increased by 25% by stretching the wire uniformly. The resistance of wire will change to (approximately)
  • a)
    12.5 Ω
  • b)
    14.5 Ω
  • c)
    15.6 Ω
  • d)
    16.6 Ω
Correct answer is option 'C'. Can you explain this answer?

Anisha Datta answered
Ω. If the wire is cut into two equal pieces, each piece will have a resistance of 20 Ω.

Explanation:

The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. When a wire is cut into two equal pieces, the length of each piece is halved. Therefore, the resistance of each piece will double because resistance is directly proportional to length.

Let's use the formula for resistance:

R = ρL/A

where R is resistance, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.

If we rearrange the formula to solve for A, we get:

A = ρL/R

Now let's plug in the values for the original wire:

R = 10 Ω
L = 10 m
ρ (for copper) = 1.68 x 10^-8 Ωm

A = (1.68 x 10^-8 Ωm)(10 m)/(10 Ω)
A = 1.68 x 10^-7 m^2

This is the cross-sectional area of the original wire. When the wire is cut into two equal pieces, each piece will have half the length and half the resistance. Therefore, the resistance of each piece will be:

R = 2(10 Ω) = 20 Ω

We can use the same formula to calculate the cross-sectional area of each piece:

A = (1.68 x 10^-8 Ωm)(5 m)/(20 Ω)
A = 4.2 x 10^-8 m^2

Since each piece has the same cross-sectional area, they are equal in diameter and length.

When a copper voltmeter is connected with a battery of e.m.f. 12 V, 2 g of copper is deposited in 30 min. If the same voltameter is connected across a 6 V bettery, then mass of copper deposited in 45 min would be
  • a)
    1 g
  • b)
    1.5 g
  • c)
    2 g
  • d)
    2.5 g
Correct answer is option 'B'. Can you explain this answer?

To solve this problem, we can use Faraday's laws of electrolysis. According to Faraday's first law, the mass of a substance deposited or liberated during electrolysis is directly proportional to the quantity of electricity passed through it.

Let's analyze the given information step by step:

1. The copper voltmeter is connected with a battery of e.m.f. 12 V, and 2 g of copper is deposited in 30 min.
2. We can calculate the quantity of electricity passed using the formula: Quantity of electricity (Q) = current (I) × time (t).
Given that the time is 30 min (0.5 hours) and the e.m.f. is 12 V, we can calculate the current using Ohm's law:
I = V/R, where V is the voltage and R is the resistance.
Let's assume the resistance is negligible, so the current (I) = V/R = 12 V/0 Ω = infinite.
Therefore, the quantity of electricity passed (Q) = I × t = infinite × 0.5 = infinite.
This means that an infinite amount of electricity is required to deposit 2 g of copper in 30 min.

Now, let's consider the second part of the question:

1. The same voltmeter is connected across a 6 V battery, and we need to find the mass of copper deposited in 45 min.
2. Using the same logic, we can calculate the quantity of electricity passed using the formula: Q = I × t.
Given that the time is 45 min (0.75 hours) and the e.m.f. is 6 V, we can calculate the current using Ohm's law:
I = V/R = 6 V/0 Ω = infinite.
Therefore, the quantity of electricity passed (Q) = I × t = infinite × 0.75 = infinite.
Again, an infinite amount of electricity is required to deposit any amount of copper.

Based on the above calculations, we can see that the quantity of electricity required to deposit copper is infinite in both cases. Therefore, no copper will be deposited when the voltmeter is connected to a 6 V battery for 45 min. Hence, the correct answer is option 'b' - 1.5 g (as given in the question).

If two bulbs of wattage 25 and 30, each rated at 220 volts, are connected in series with a 440 volt supply, which bulb will fuse
  • a)
    25W bulb
  • b)
    30W bulb
  • c)
    Neither of them
  • d)
    Both of them
Correct answer is option 'A'. Can you explain this answer?

Aman Dasgupta answered
Explanation:

When two bulbs of different wattage are connected in series, the bulb with lower wattage will consume less power and hence have a higher resistance compared to the other bulb. This means that the lower wattage bulb will have a higher voltage drop across it and hence will be more prone to fuse.

In this case, the 25W bulb has a higher resistance compared to the 30W bulb and hence will have a higher voltage drop across it. So, the 25W bulb will fuse first.

Answer: option 'A' - 25W bulb will fuse.

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