Physics Test

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Physics Test - 5

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Question 1
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Directions: The following question has four choices, out of which ONE or MORE can be correct.

A uniform bar of length 6a and mass 8m lies on a smooth horizontal table. Two point masses m and 2m moving in the same horizontal plane with speed 2 v and v, respectively, strike the bar [as shown in the figure] and stick to the bar after collision. Denoting angular velocity (about the centre of mass), total energy and centre of mass velocity respectively by ω, E and v_c, we have after collision:

A
v_c = 0

B
ω = 3v/5a

C
ω = v/5a

D
E = 3/5 mv²

Solution
Question 2
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In Doppler's effect in sound,

A
the apparent change in frequency received by stationary observer is more in the case of a source moving towards than away from the observer

B
it is not possible to detect any change in frequency when the speed of source or observer is more than that of sound

C
wind alone cannot produce any Doppler's effect

D
the wavelength always changes when there is some relative motion between the source and the observer

Solution
Question 3
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The specific heat of 100 gm of a substance varies with temperature T as c = AT² + BT cal/gm/K with absolute temperature. [Given A = 2.1 10^-3 cal/g (^oC)³; B = 15 10^-2 cal/g (^oC)²].

A
The amount of heat required to raise the temperature from 320 K to 350 K is 1858240 cal.

B
The amount of heat required to raise the temperature from 320 K to 350 K is 858240 cal.

C
The time taken if the heat is supplied by a heater of resistance 300 ohm operating on 200 V is 7.5 hrs.

D
The specific heat of the substance increases non-linearly with temperature

Solution
Question 4
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A
the magnetic moment of electron revolving in anti-clockwise direction decreases

B
the magnetic moment of electron revolving in anti-clockwise direction increases

C
the magnetic Lorentz force on the electron revolving clockwise tends to increase the centripetal force

D
the magnetic Lorentz force on the electron revolving clockwise tends to decrease the centripetal force

Solution
Question 5
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A non conducting ring of radius R is rotating about an axis passing through its centre and perpendicular to its plane with an angular velocity ω . Charge q is uniformly distributed over its surface.

A
The magnetic moment of the ring is qωR2/2.

B
The magnetic field produced at the centre is u₀ qf/2R

C
The magnetic field and the area vector are in opposite directions.

D
The magnetic field produced is uniform at the centre.

Solution
Question 6
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Directions: The following question has four choices, out of which ONE or MORE can be correct.

A solid sphere of uniform density and radius 4 units is located with its centre at the origin O of coordinates. Two spheres of equal radii 1 unit, with their centres respectively at A (-2, 0, 0) and B (2, 0, 0), are taken out of the solid leaving behind spherical cavities as shown in the figure. Then,

A
the gravitational field due to this object at the origin is zero

B
the gravitational field at the point B (2, 0, 0) is zero

C
the gravitational potential is same at all points of the circle y² + z² = 36

D
the gravitational potential is same at all points on the circle y² + z² = 4

Solution

Due to the solid sphere of a uniform density, gravitational field is zero at the centre of the sphere. The cavities A and B can be treated as negative masses and they are situated on opposite sides of the centre O. Hence, gravitational forces exerted by the cavity masses on a mass at O are opposite in direction. Hence, resultant force on mass at O is zero. Thus, gravitational force due to this object at the origin O is zero.

Consider a circle y² + z² = 36; the centre of the circle is (0,0,0) and the radius of the circle is 6 units. The circle lies in y-z plane. For the point outside the sphere or situated at the sphere, the mass of the sphere can be assumed to be situated at the centre. All the points of the circle y² + z²= 36 are equidistant from the centre; hence, gravitational potential is same at all the points in the given circle.

Consider the circle y² + z² = 4; its centre lies at (0, 0, 0) and the radius is 2 units. It lies in y-z plane perpendicular to x-axis. All the points of the circle y² + z² = 4 are equidistant from the centre; hence, gravitational potential is same at all the points in the given circle.
Question 7
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The photon emitted in n = 3 to n = 1 transition in He⁺ hits a photosensitive surface of threshold wavelength 6000 A°. The photoelectrons emitted will have __________.

A
a minimum wavelength of (approx.) 2.0 A° associated with it

B
a stopping potential of (approx) 38.5 V

C
photoelectron that will be emitted in 10^-10 seconds time

D
All are correct

Solution
Question 8
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A cart is moved horizontally at a constant velocity of 4 m/sec. A ball is thrown from it at a velocity of 4 m/sec and at an angle horizontally with respect to the cart. Assume that the height of the cart is very small, such that the motion of the ball is assumed to be a ground to ground projectile. If the horizontal range of the ball with respect to the ground is R1 and with respect to the cart is R2, then ______________.

A
R₁ will be maximum forθ = 90^o

B
R₁ will be maximum forθ = 60o

C
R₂ will be maximum forθ = 45o

D
All are correct

Solution
Question 9
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For an ideal diatomic gas, the P-V diagrams are shown. The various quantities indicated in the columns are calculated. The relative values are also given.

In which graph, the energy change is 225 J and the heat capacity is more than C_V?

A
(I) (i) (R)

B
(II) (iii) (S)

C
(IV) (ii) (Q)

D
(III) (iv) (P)

Solution