Physics Test

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Physics Test - 4

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Question 1
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Directions: From the statements of Assertion and Reason mark the correct answer from the options.

(a) If both assertion and reason are true, and reason is the correct explanation of assertion.

(b) If both assertion and reason are true, but reason is not the correct explanation of assertion.

(c) If assertion is true, but reason is false.

(d) If both assertion and reason are false.

Assertion: Diamagnetic materials can exhibit magnetism.

Reason: Diamagnetic materials have permanent magnetic dipole moment.

A
(a)

B
(b)

C
(c)

D
(d)

Solution

Some materials when placed in an external magnetic field, acquire a very low magnetism in a direction opposite to the field. These materials when brought near the end of a strong magnet, they get repelled. These materials are diamagnetic and this property of materials is called the diamagnetism. This property is generally found in materials in which there are even number of electrons in their atoms (or molecules) and pairs are formed with two electrons. In each pair, the spin of one electron is in direction opposite to the spin of other electron. Hence, the electrons of each pair completely cancel the magnetic moment of each other. Thus, the net magnetic moment of each atom of such material is zero. Hence, option (c) is true.
Question 2
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A magnet of magnetic moment M and length 2l is bent at its mid-point such that the angle of bending is 60^o. Now, the magnetic moment is

A
M

B
2M

C
M/2

D
M/√2

Solution
Question 3
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A toy of mass M₁ is pulled along a horizontal frictionless surface by rope of mass M₂. A force F is applied to the free end of the rope. the force exerted on the toy is:

A
F

B
M₁F/(M₁ + M₂)

C
M₁F/(M₁ - M₂)

D
M₂F/(M₁ + M₂)

Solution

a = F/(M₁ + M₂)

force on mass M₁ = M₁ × a = M₁F/(M₁+ M₂)
Question 4
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A long horizontal rod has a bead, which can slide along its length and is initially placed at a distance L from one end A of the rod. The rod is set in angular motion about A with constant angular acceleration α . If the coefficient of friction between the rod and the bead is and gravity is neglected, then the time after which the bead starts slipping is

A

B

C

D
infinitesimal

Solution
Question 5
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Two weights 'w₁' and 'w₂' are suspended by two strings on a frictionless pulley. When the pulley is pulled up with an acceleration 'g', then the tension in the string is

A

B

C

D

Solution

Let m₁ > m₂.

As the lift is accelerating with acceleration (a = g), then the tension in the string is
Question 6
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Directions: The following question has four choices out of which ONLY ONE is correct.

An open knife edge of mass M is dropped from a height 'h' on a wooden floor. If the blade penetrates 's' into the wood, the average resistance offered by the wood to the blade is

A
Mg

B

C

D

Solution
Question 7
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A stone is dropped from a certain height. After falling for 5 sec, the stone breaks through a pane of glass and instantaneously, loses half of its velocity. If the stone takes one more second to reach the ground, what is the height of the glass above the ground? (Given g = 10 m/s²)

A
60 m

B
50 m

C
30 m

D
20 m

Solution
Question 8
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We wish to see inside an atom. Assume the atom to have a diameter of 100 pm. This means that one must be able to resolve a width of say 10 pm. If an electron microscope is used, the energy required should be

A
1.5 keV

B
15 keV

C
150 keV

D
1500 keV

Solution
Question 9
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The half-life of ¹³¹I is 8 days. If we have a sample of ¹³¹I at time t = 0, we can assert that

A
no nucleus will decay before t = 4 days

B
no nucleus will decay before t = 8 days

C
all nuclei will decay before t = 16 days

D
a given nucleus may decay any time after t = 0

Solution
Question 10
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A radioactive nuclide can decay simultaneously by two different processes, which have individual decay constantsλ₁ anaλ₂ . The effective decay constant of the nuclide (λ) is given by

A

B

C

D

Solution

The effective decay constant of the nuclide is given by λ₁ + λ₂
Question 11
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The binding energies for nuclei ₁H¹, ₂He⁴, ₂₆Fe⁵⁶and ₉₂U²³⁵ are 2.22, 28.3, 492 and 17.86 MeV, respectively. The most stable nucleus is

A
₁H¹

B
₂He⁴

C
₂₆Fe⁵⁶

D
₉₂U²³⁵

Solution

As the binding energy of Fe⁵⁶ is highest, so the most stable nucleus will be₂₆Fe⁵⁶.
Question 12
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The binding energy per nucleon of ₁H² is 1.1 MeV and binding energy per nucleon of ₂He⁴ is 7 MeV. The energy released when two ₁H² combine to form ₂He⁴ is

A
6.8 MeV

B
30.2 MeV

C
23.6 MeV

D
None of these

Solution

Energy Absorbed to break apart 2₁H² atoms = 1.1 × 4 = 4.4 MeV

Energy Released in formation of 1 ₂He⁴ atom = 7 × 4 = 28 MeV

Hence, energy released = (28 - 4.4) MeV = 23.6 MeV
Question 13
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For a certain radioactive substance, it is observed that after 4 hours, only 6.25% of the original sample is left undecayed. Which of the following statements is incorrect?

A
The half life of the sample is 1 hr.

B
The mean life of the sample is 1/2 hr.

C
The decay constant of the sample is (ln 2) hr^-1.

D
After further 4 hours, the amount of the substance leftover would be only 0.39% of the original amount.

Solution
Question 14
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Li nucleus has three protons and four neutrons. Mass of lithium nucleus is 7.016005 amu. Mass of proton is 1.007277 amu and mass of neutron is 1.008665 amu. Mass defect for lithium nucleus in amu is

A
0.04048 amu

B
0.04059 amu

C
0.04062 amu

D
0.04055 amu

Solution
Question 15
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During the adiabatic expansion of 2 moles of a gas, the internal energy was found to have decreased by 100 J. The work done by the gas in this process is

A
zero

B
- 100 J

C
200 J

D
100 J

Solution

dU = 100 J

dQ = dU + dW

dQ = 0 (Adiabatic process)

dW = -dU = + 100 J