Physics Test

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Physics Test - 26

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Weekly Quiz Competition

Question 1
3 / -1

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 2
3 / -1

A police car horn emits sound at a frequency of $240 H z$ when the car is at rest. If the speed of sound is $330 m / s$ , the frequency heard by an observer who is approaching the car at a speed of $11 m / s$ is:

A
$248 H z$

B
$244 H z$

C
$240 H z$

D
$230 H z$

Solution

Given, $v = 330 m / s, v_{0} = 11 m / s, n = 240 H z$

Frequency heard by the observer,

$n' = n (\frac{v + v_{0}}{v})$

$= 240 (\frac{330 + 11}{330})$

$= 248 H z$
Question 3
3 / -1

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
$\sqrt{\frac{μ}{α}}$

B
$\frac{μ}{\sqrt{α}}$

C
$\frac{1}{\sqrt{μ α}}$

D
infinitesimal

Solution

The radius of the circular motion of the bead is $r = L$ . The linear acceleration of the bead is $a = α r = α L$ .

If $m$ is the mass of the bead, then

Force acting on the bead $= m a = m α L$

Reaction force acting on the bead is $R = m α L$

This bead starts slipping when the frictional force between the bead and the rod becomes equal to centrifugal force acting on the bead, i.e.,

$μ R = \frac{m v^{2}}{r}$

or $μ m α L = m r ω^{2} = m L ω^{2} (∵ v = r ω)$

or $μ α = ω^{2} = {(α t)}^{2} (∵ ω = α t)$

or $μ α = α^{2} t^{2}$ or $t = \sqrt{\frac{μ}{α}}$
Question 4
3 / -1

Directions: The following question contains 4 choices (A), (B), (C), and (D), out of which ONLY ONE is correct.

In the experiment to determine the speed of sound using a resonance column is:

A
prongs of the tuning fork are kept in a vertical plane

B
prongs of the tuning fork are kept in a horizontal plane

C
in one of the two resonances observed, the length of the resonating air column is close to the wavelength of sound in air

D
in one of the two resonance observed, the length of the resonating air column is close to half of the wavelength of sound in air

Solution

In an experiment to determine the speed of sound using a resonance column, prongs of the tuning fork are kept in a vertical plane so that both the prongs can send sound waves inside the tube.

In one resonance the length of the resonating air column is,

$l_{1} = \frac{λ}{4}$

And in another resonance the length of the resonating air column is,

$l_{2} = \frac{3 λ}{4}$
Question 5
3 / -1

What is the dimension of $\frac{L}{R C V}$ , where $L, R, C$ , and $V$ have their usual meanings?

A
$M^{1} L^{1} A^{- 2} T^{0}$

B
$M^{0} L^{- 1} A^{- 1} F^{1}$

C
$M^{1} L^{0} A^{- 1} T^{0}$

D
$M^{0} L^{0} A^{- 1} T^{0}$

Solution

$e m f = V = L \frac{d I}{d t}$

$L = V \frac{d t}{d I}$

$R C$ is time constant. Its dimension is equal to time.

So, dimension of $\frac{L}{R C V} = V \frac{d t}{d I}$

$R C V = \frac{1}{A} = M^{0} L^{0} A^{- 1} T^{0}$
Question 6
3 / -1

A magnet of magnetic moment $M$ and length $2 l$ is bent at its mid-point such that the angle of bending is $60 °$ . Now, the magnetic moment is:

A
$M$

B
$2 M$

C
$\frac{M}{2}$

D
$\frac{M}{\sqrt{2}}$

Solution

In the new situation, we have

As the length of the magnet is halved, Magnetic Moment $M' = m (l) = \frac{M}{2}$

The magnetic moment is a vector quantity.

$M = \sqrt{M_{1}^{2} + M_{2}^{2} + M_{1} M_{2} \cos θ}$

$M = \sqrt{\frac{M^{2}}{4} + \frac{M^{2}}{4} + \frac{2 M^{2}}{4} \cos 120 °}$ (angle between the vectors would be $120 °$ )

$M = \frac{M}{2}$
Question 7
3 / -1

An observer is moving towards a stationary source with $\frac{1}{10}$ the speed of sound. The ratio of apparent frequency to real frequency is:

A
$\frac{11}{10}$

B
$\frac{10}{9}$

C
${(\frac{11}{10})}^{2}$

D
${(\frac{9}{10})}^{2}$

Solution

Frequency, as observed by the observer is

$f = [\frac{v + v_{0}}{v}] f_{0}$ , where $v_{0}$ is the speed of the observer, $v$ is the speed of the sound.

$\frac{f}{f_{0}} = [\frac{v + v_{0}}{v}] = \frac{v + \frac{v}{10}}{v}$

$\frac{f}{f_{0}} = \frac{11}{10}$
Question 8
3 / -1

Two SHMs are respectively represented by $y_{1} = a \sin (ω t - k x)$ , and $y_{2} = b \cos (ω t - k x)$ . The phase difference between the two is:

A
$\frac{π}{2}$

B
$\frac{π}{4}$

C
$\frac{π}{6}$

D
$\frac{3 π}{4}$

Solution
Question 9
3 / -1

A coil takes a current of $2 A$ and $200 W$ power from an alternating current source of $220 V, 50 H z$ . What is the inductance of the coil?

A
$0.312 H$

B
$0.142 H$

C
$0.285 H$

D
$1.07 H$

Solution

Given,

$P = 200 W, I = 4 A, V = 220 V$ and $f = 50 H z$

We know that, $R = \frac{P}{I^{2}}$

$= \frac{200}{4} = 50 Ω$

$Z = \sqrt{R^{2} + X_{L}^{2}} = \sqrt{{(50)}^{2 + X_{L}^{2}}}$

$Z = \frac{V}{I} = \frac{220}{2} = 110 Ω$

$X_{L}^{2} = 12100 - 2500 = 9600$

$X_{L} = 98 Ω$

$L = \frac{X_{L}}{ω} = \frac{X_{L}}{2 πf}$

$= \frac{98}{2 \times 3.14 \times 50}$

$= 0.312 H$
Question 10
3 / -1

$L i$ nucleus has three protons and four neutrons. Mass of lithium nucleus is $7.016005 a m u$ . The mass of proton is $1.007277 a m u$ and the mass of a neutron is $1.008665 a m u$ . A mass defect for lithium nucleus in $a m u$ is:

A
$0.04048 a m u$

B
$0.04059 a m u$

C
$0.04062 a m u$

D
$0.04055 a m u$

Solution

We know that,

Mass defect $=$ mass of nucleons $-$ a mass of the nucleus

$= (3 \times 1.007277 + 4 \times 1.008665) - 7.016005$

$= 0.040486 a m u$

$\approx 0.04050 a m u$

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Physics Test - 26

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Physics Test - 26

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Question 1

no nucleus will decay before t=4 days

no nucleus will decay before t=8 days

all nuclei will decay before t=16 days

a given nucleus may decay any time after t=0

Solution

Question 2

248Hz

244Hz

240Hz

230Hz

Solution

Question 3

μα

μα

1μα

infinitesimal

Solution

Question 4

prongs of the tuning fork are kept in a vertical plane

prongs of the tuning fork are kept in a horizontal plane

in one of the two resonances observed, the length of the resonating air column is close to the wavelength of sound in air

in one of the two resonance observed, the length of the resonating air column is close to half of the wavelength of sound in air

Solution

Question 5

M1L1A-2T0

M0L-1A-1F1

M1L0A-1T0

M0L0A-1T0

Solution

Question 6

M

2M

M2

M2

Solution

Question 7

1110

109

11102

9102

Solution

Question 8

π2

π4

π6

3π4

Solution

Question 9

0.312H

0.142H

0.285H

1.07H

Solution

Question 10

0.04048amu

0.04059amu

0.04062amu

0.04055amu

Solution

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no nucleus will decay before $t = 4$ days

no nucleus will decay before $t = 8$ days

all nuclei will decay before $t = 16$ days

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

$248 H z$

$244 H z$

$240 H z$

$230 H z$

$\sqrt{\frac{μ}{α}}$

$\frac{μ}{\sqrt{α}}$

$\frac{1}{\sqrt{μ α}}$

$M^{1} L^{1} A^{- 2} T^{0}$

$M^{0} L^{- 1} A^{- 1} F^{1}$

$M^{1} L^{0} A^{- 1} T^{0}$

$M^{0} L^{0} A^{- 1} T^{0}$

$M$

$2 M$

$\frac{M}{2}$

$\frac{M}{\sqrt{2}}$

$\frac{11}{10}$

$\frac{10}{9}$

${(\frac{11}{10})}^{2}$

${(\frac{9}{10})}^{2}$

$\frac{π}{2}$

$\frac{π}{4}$

$\frac{π}{6}$

$\frac{3 π}{4}$

$0.312 H$

$0.142 H$

$0.285 H$

$1.07 H$

$0.04048 a m u$

$0.04059 a m u$

$0.04062 a m u$

$0.04055 a m u$