Physics Test 126

Result

Physics Test 126

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Question 1
4 / -1

Three charges e, e and - 2e are placed at the corners of the triangle as shown. The net dipole moment of the system is

A

B
Zero

C

D

Solution

At A, the x-components of the two dipole moments cancel and y-components add
Question 2
4 / -1

A mass is attached to one end of a spring of spring constant k. The spring is stretched and then released such that its amplitude of oscillation is A. For a displacement y from the mean position, if the kinetic energy is 44% of its potential energy, then y in terms of A is

A

B

C

D

Solution
Question 3
4 / -1

At a given instant there are 25% of undecayed radioactive nuclei in a sample. After 20s, the number of undecayed nuclei reduces to 12.5%. The extra time required in which the number of undecayed nuclei will further reduce to 3.125% of the sample is-

A
60 sec

B
80 sec

C
40 sec

D
120 sec

Solution

Half-life of the radioactive sample, t_1/2 = time in which the number of undecayed nuclei becomes half = 20 sec (given).
The material further reduces to 3.125% in n half-lives is given by

where N_fis % of undecayed nuclie after n half lifes , and A is % of undecayed nuclie initially.
here N_f= 3.125 %
and N_i = 12.5 %

so time taken t = nt_1/2= 2 x 20 = 40 second
Question 4
4 / -1

The escape velocity for an atmospheric particle 2000 km above the earth's surface is (Radius of the earth = 6.4 x 10⁶ m and g = 10 m s^{- 2} )

A
9.68 Kms^-1

B
9.78 Kms^-1

C
9.88 kms^-1

D
9.98 Kms^-1

Solution
Question 5
4 / -1

A circular disc of radius r and thickness r/6 has moment of inertia I about an axis passing through its centre and perpendicular to its plane. It is melted and recasted to a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is

A
I/2

B
2I/11

C
I/10

D
I/5

Solution

Volume oc circular disc = surface of area x thickness

The mass of the circular disc and sphere are the same

where R is the radius of the sphere,

Moment of interia of a circluar disc

Moment of interia of solid sphere
Question 6
4 / -1

When an UV light of 10¹⁵ Hz and intensity 2 W/m² is directed at a metal surface, photoelectrons emitted were found to have a maximum kinetic energy of 1.6 eV. If the work functions for different materials are as follows: Potassium 2.2 eV, Sodium 2.3 eV, Lithium 2.5 eV and Calcium 3.2 eV, identify the metal in the given problem.

A
Lithium

B
Calcium

C
Sodium

D
Potassium

Solution

E = hv = 6.63 x 10^-34x10¹⁵
=6.63 x 10^-19J
= 4.1 eV
( dividing by e = 1.6 x 10^-19)
E_max=hv - hv₀
⇒ hv₀= 4.1 - 1.6
= 2.5 eV
⇒ Lithium
Question 7
4 / -1

Two sources of sound S₁ and S₂ each emitting waves of wavelength A are kept symmetrically on either side of the centre 0 of a circle ABCD such that S₁O = S₂O = K . When the detector is moved along the circumference of the circle, the number of maxima recorded by the detector in one revolution is

A
24

B
18

C
12

D
8

Solution

For the point A, the path difference is zero and for the point B, it is 2 λ. In between A and B there will be a point E where the path difference is λ.

Hence at the points A, E and B there will be maximum sound due to S₁ and S₂.
In a circular path, it will be easier to locate points like F, C, G, D and H so that the total number of maxima amounts to 8.
Question 8
4 / -1

A boat capable of a speed v in still water wants to cross a river of width d. The speed of the water current increases linearly from zero at either bank to a maximum of u at the middle of the river. When the boat is rowed at right angles to the bank, its downstream drift is

A

B

C

D

Solution

Let us choose a coordinate system with its origin as the starting point of the boat, the + x-axis points downstream and + y-axis points at right angles to the bank of the river.

x-motion of the boat is due to the water current velocity vcurrent while the y-motion is caused solely by the velocity v of the boat.
The above two motions are independent of each other and can be treated separately.
Assuming that the boat starts at time t = 0, the y coordinate after a time t is y = v t ... (i)

The speed of water current is a function of y and is given by

Substituting for y from equation (i)
By symmetry, its value at the middle of the river is D/2.

The time required to reach the middle of the river is

Separating the variable in equation (iii) and intergrating
Question 9
4 / -1

Figure shows the plot of a potential energy function of a conservative system U versus x. Which of the following statements is correct ?

A
The force has the greatest magnitude at point E₂.

B
The force is positive and greater than zero at points E₁, E₂. E₃ and E₄.

C
The system is in stable equilibrium at E_3.

D
The system is in neutral equilibrium at E₁.

Solution

Force F versus x is drawn in figure. At points E₁points E₁,E2,E₃and E₄
F=0
F has the greatest magnitude nearer to point E₁.

If U is minimum i.e., = positive, equilibrium is stable.
Question 10
4 / -1

A sphere with some cavity has outer radius R. It rolls down an inclined plane without slipping and attains a speed v at the bottom. When this sphere slides down without rolling on the frictionless inclined plane of same height its speed at the bottom is 5v/4. The radius of gyration of the sphere is

A
3R/4

B
3R/2

C
R/4

D
R/2

Solution

Let k be the radius of gyration and M the mass of the sphere. The kinetic energy should be the same in both the cases