Physics Test

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Physics Test - 5

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Question 1
1 / -0

A disk of radius a/4 having a uniformly distributed charge 6C is placed in the x-y plane with its centre at (−a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from x = a/4 to x = 5a/4. Two point charges −7C and 3C are placed at (a/4, −a/4, 0) and (−3a/4, 3a/4, 0), respectively. Consider a cubical surface formed by six surfaces x = ± a/2, y = ± a/2, z = ± a/2. The electric flux through this cubical surface is

A

−2C/ε0

B

10C/ε0

C

2C/ε0

D

12C/ε0
Question 2
1 / -0

The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is

A

k2 A/(k1 + k2)

B

k2 A/k1

C

k1 A/(k1 + k2)

D

k1 A/k2
Question 3
1 / -0

When liquid medicine of density ρ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When the force becomes smaller than the weight of the drop, the drop gets detached from the dropper. If the radius of the opening of the dropper is r, the vertical force due to the surface tension on the drop of radius R (assuming r << R) is

A

(2πr^2 T)/R

B

(2πr^2 T)/r

C

2πrT

D

2πRT
Question 4
1 / -0

Photoelectric effect experiments are performed using three different metal plates p, q and r having work functions φp = 2.0 eV, φq = 2.5 eV and φr = 3.0 eV, respectively. A light beam containing wavelengths of 550 nm, 450 nm and 350 nm with equal intensities illuminates each of the plates. The correct I-V graph for the experiment is : (Take hc = 1240 eV nm)

A

option A

B

Option D

C

Option B

D

Option C
Question 5
1 / -0

A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards it is subjected to a time-dependent force F(t) in the x direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is

A

5.06 J

B

14.06 J

C

7.50 J

D

4.50 J
Question 6
1 / -0

A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it upto height H. Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes out from the orifice and the water level in the vessel becomes steady with height of water column being 200 mm. Find the fall in height (in mm) of water level due to opening of the orifice. [Take atmospheric pressure = 1.0 × 10^5 N/m^2 , density of water = 1000 kg/m^3 and g = 10 m/s^2. Neglect any effect of surface tension.]

A

6

B

7

C

8

D

5
Question 7
1 / -0

A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is

A

real and at a distance of 16 cm from the mirror

B

virtual and at a distance of 16 cm from the mirror

C

virtual and at a distance of 20 cm from the mirror

D

real and at a distance of 20 cm from the mirror
Question 8
1 / -0

A solid sphere of radius R has a charge Q distributed in its volume with a charge density ρ = kr^a, where k and a are constants and r is the distance from its centre. If the electric field at r = R/2 is 1/8 times that at r = R, find the value of a.

A

2

B

3

C

4

D

1
Question 9
1 / -0

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses m, 2m and m, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B makes completely inelastic collision with C. All motions occur on the same straight line. Find the final speed (in m/s) of the object C.

A

4

B

3

C

5

D

6
Question 10
1 / -0

When a particle is restricted to move along x-axis between x = 0 and x = a, where a is of nanometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends x=0 and x=a. The wavelength of this standing wave is related to the linear momentum p of the particle according to the de Broglie relation. The energy of the particle of mass m is related to its linear momentum as E = p^2 /2m. Thus, the energy of the particle can be denoted by a quantum number ‘n’ taking values 1, 2, 3, …. (n = 1, called the ground state) corresponding to the number of loops in the standing wave. Use the model described above to answer the following three questions for a particle moving in the line x = 0 to x = a. Take h = 6.6 × 10^-34 Js and e = 1.6 × 10^-19 C.The speed of the particle that can take discrete values is proportional to

A

n

B

n^-1

C

n^1/2

D

n^-3/2