1 Atoms and Nuclei
If the average life time of an excited state of hydrogen is of the order of 10−8s, estimate how many orbits an electron makes when it is in the state n=2 before it suffers a transition to state n=2 (Bohr radius a0=5.3×10−11m) ?
1) 8×106 2) 6×106 3) 8×104 4) 8×105
The velocity of $$e^-$$ in $$2nd$$ orbit of $$H^-$$ atom, $$U=1.09 \times 10^8cm/s$$ The orbit frequency to be $$\dfrac{Velocity \ of \ e^-}{2\pi r_3} =\dfrac{\mu}{2xr_2}$$ $$t=\dfrac{1.09 \times 10^8}{2 \times 3.14 \times 0.529 \times 10^{-8}\times 4}$$ $$t=8.2\times 10^{14}/8$$ The number of orbits made by the $$=8.2\times 10^{14}/8 \times 10^{-8}$$ $$8\times 10^6$$
2 Gravitation
The average distances of two planets (Neptune and Saturn) from the sun are 1031m and 1032 m respectively. The ratio of time periods of the planets will be: 1) 100:1 2) 1:10√10 3) √10:1 4) 10√10:1
By Kepler's third law, $$T^2 \propto a^3$$
3 Current Electricity
The voltage versus current plot for an ideal power supply should:
(1) have voltage linearly proportional to current.
(2) have voltage independent of current (for a specified polarity).
(3) have a voltage response similar to a zener diode.
(4) cover a wide range of voltage and current
4 Physical world and measurement
A physical parameter a can be determined by measuring the parameters b, c, d and e using the relation a = bα cβ / dγ eδ. If the maximum errors in the measurement of b, c,d and e are b1%, c1%, d1% and e1 %, then the maximum error in the value of a determined by the experiment is 1) (b1 + c1 + d1 + e1)% 2) (b1 + c1 – d1 – e1)% 3) (αb1 + βc1 – γd1 – δe1)% 4) (αb1 + βc1 + γd1 + δe1)%
Solution
5 Electronic Devices
Function of a grid in a triode is :
(1) to increase plate voltage
(2) to decrease plate voltage
(3) to reduce the effect of space charge
(4) None
6 Waves
A wave of amplitude 10 cm and frequency 1000 Hz is travelling with a velocity of 300 m/s. Calculate the phase difference of a particle at a distance of 3 m from the origin after 1.001 s
1) 20π 2) 19π 3) 18π 4) 8π
Wave number
K=ω? / v
Phase difference is
?=Kx−ωt
= 18π
7 Kinematics
How far will a brick starting from rest fall freely in 3.0 seconds? 1) 15 m 2) 29 m 3) 44 m 4) 88 m
d=vit+1/2at2. The block starts from rest so the initial velocity is zero. The equation becomes d=1/2at2. The only acceleration the brick feels is the acceleration due to gravity = 9.81m/s2
8 Electromagnetic Waves
Relative permeability and relative permitivity of a medium are respectively $$4$$ and $$9$$. If the magnetic induction field of the electromagnetic wave travelling in the medium is $$4.2 \times { 10 }^{ -8 }T$$, then the magnitude of its electric field is
1) $$4.2V{ m }^{ -1 }$$ 2) $$2.1\times { 10 }^{ -8 }V{ m }^{ -1 }$$ 3) $$4.2\times { 10 }^{ -8 }V{ m }^{ -1 }$$ 4) $$2.1V{ m }^{ -1 }$$
The speed of light in the medium, $$v=\dfrac{c}{\sqrt{\mu_r\epsilon_r}}$$ $$= 0.5 \times\dfrac{3\times 10^{8}m/s}{\sqrt{(4)(9)}}$$ $$=10^{8}m/s$$
9 Oscillations
A mass M attached to a spring oscillates with a period of 2s. If the mass is increased by 4 kg, the period increases by 1s. The initial mass M in kg assuming that Kooke’s law is obeyed is: 1) 1.6 2) 2.4 3) 3.2 4) 4.0
$$\displaystyle{2}={2}\pi\sqrt{{\frac{{{M}}}{{{k}}}}}$$ -- (i)
$$\displaystyle{3}={2}\pi\sqrt{{\frac{{{M}+{4}}}{{{k}}}}}$$ -- (ii)
Solving two equations, we get M=3.2kg
10 Work Energy and Power
Two marbles, one twice as heavy as the other, are dropped to the ground from the roof of a building. Just before hitting the ground, the heavier marble has:
1. Twice as much kinetic energy as the lighter one.
2. The same kinetic energy as the lighter one.
3. Four times as much kinetic energy as the lighter one.
4. Half as much kinetic energy as the lighter one.
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