Physics Test

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Physics Test - 17

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Question 1
4 / -1

A mass M is hung with a light spring. If the extra mass m is also hung with spring, the spring is stretched by x cm. Then, the time period of including mass will be

A
\(T=2 \pi \sqrt{\frac{M+m i x}{m g}}\)

B
\(T=2 \pi \sqrt{\frac{m g}{x(M+m)}}\)

C
\(\mathrm{T}=2 \pi \sqrt{\frac{M+m}{m g x}}\)

D
\(T=\frac{\pi}{2} \sqrt{\frac{m g}{x(M+m)}}\)

Solution

In first case, when mass \(\mathrm{M}\) is attached let the extension in the spring is \(\mathrm{y}\).
At equilibrium \(\mathrm{Mg}=\mathrm{ky}\) -1
Where \(k\) is the spring constant.
In second case, when additional mass \(m\) is attached let the extra extension in the spring is \(x\) At equilibrium \((M+m) g=k(x+y) \quad \rightarrow 2\)
From 1 and 2 we have
\(m g=k x \Rightarrow k=\frac{m g}{x}\)
Time period of oscillation is \(T=2 \pi \sqrt{\frac{M+m}{k}} \Rightarrow T=2 \pi \sqrt{\frac{M+m x}{m g}}\)
Question 2
4 / -1

A cart of 100 kg is free to move on smooth rails and a block of 20 kg is resting on it. The surface of contact between the cart and the block is smooth. A force of 60 N is applied to the cart. Acceleration of 20 kg block in m/s2 is

A
3

B
0.6

C
0.5

D
0

Solution

\(M=\) Mass of cart \(=100 \mathrm{kg}\)
\(\mathrm{m}=\) mass of block \(=20 \mathrm{kg}\)
a = required acceleration
\(F=(M+m) a\)
\(\Rightarrow 60=120 \mathrm{a}\)
\(\Rightarrow \mathrm{a}=0.5\)
Acceleration \(=\mathrm{a}=0.5 \mathrm{m} / \mathrm{s}^{2}\)
Question 3
4 / -1

Three progressive waves A, B and C are shown in the figure.

With respect to A, the progressive wave

A
\(\mathrm{B}\) lags by \(\frac{\pi}{2}\) and \(\mathrm{C}\) leads by \(\frac{\pi}{2}\)

B
B lags by π and C leads by π

C
B leads by \(\frac{\pi}{2}\) and \(C\) lags by \(\frac{\pi}{2}\)

D
B leads by π and C lags by π

Solution
Question 4
4 / -1

Directions: From the statements of Assertion and Reason mark the correct answer from the options:

(a) If both assertion and reason are true and reason is the correct explanation of assertion.

(b) If both assertion and reason are true but reason is not the correct explanation of assertion.

(c) If assertion is true but reason is false.

(d) If both assertion and reason are false

Assertion: A ladder is more apt to slip, when you are high up on it than when you just begin to climb.

Reason: High up on a ladder, the torque is large and on climbing up the torque is small.

A
A

B
B

C
C

D
D

Solution

Here both reason and assertion are correct and reason is correct explanation of the assertion. Since torque is directly proportional to the value of displacement vector, so value of torque is maximum when a person is at the top. On the other hand, value of displacement vector is minimum when a person is just going to climb, so 1^st option is the answer.
Question 5
4 / -1

The power dissipated across an 8Ω resistor in the circuit shown here is 2 W. The power dissipated (in watts) across a 3Ω resistor is:

A
2.0

B
1.0

C
0.5

D
3.0

Solution

We know \(P=\frac{V^{2}}{R}\)
For \(8 \Omega\) resistance, we have
\(v^{2}=2 \times 8=16\)
\(V=4\)
We know that voltage is same in parallel combination of resistors. So, current through upper limb having equivalent resistance of \(4 \Omega\) (resistances \(1 \Omega\) and \(3 \Omega\) are in series), \(I=\frac{V}{R}=\frac{4}{4}=1 A\)
Now, current through \(3 \Omega\) resistance will also be 1 A.
So, power across \(3 \Omega\) resistor \(=1^{2} R=3\) watts
Question 6
4 / -1

A sonometer wire of density 'd' and radius 'a' is held between two bridges at a distance 'l' apart. The wire has a tension 'T'. The fundamental frequency of the wire is

A
\(\mathrm{n}=\frac{1}{l} \sqrt{T \pi a^{2} d}\)

B
\(n=\frac{1}{2 l} \sqrt{\pi a^{2} d}\)

C
\(\mathrm{n}=\frac{T}{2 l} \sqrt{\pi a^{2} d}\)

D
\(n=\frac{1}{2 l} \sqrt{\frac{T}{\pi a^{2} d}}\)

Solution

In case of the sonometer wire, the two bridge points are treated as clamped points. So, the
fundamental wavelength is \(\lambda=2\).
Corresponding fundamental frequency, \(n=\frac{v}{\lambda}=\frac{v}{21}\)
Velocity of the wave in the string,
\(v=\sqrt{\frac{T}{\mu}},\) where \(T\) is the tension in the wire and \(\mu\) is the mass per unit length.
If 'd' is the density of the wire,

Then, \(d=\frac{m}{V}=\frac{m}{A l} ;\) where \(A\) is the cross-sectional area of the wire \(\left(A=\pi a^{2}\right)\)
\(\mathrm{d}=\frac{\mathrm{\mu}}{\mathrm{A}} \Rightarrow \mu=\mathrm{Ad}\)
\(v=\sqrt{\frac{T}{A d}}\)
So, \(n=\frac{1}{21} \sqrt{\frac{T}{A d}}\)
or \(n=\frac{1}{2 l} \sqrt{\frac{T}{\pi a^{2} d}}\)
Question 7
4 / -1

ABC is a triangle, forces P, Q, R act along the lines OA, OB and OC and are in equilibrium. If O is in the centre of ABC, then

A
\(\frac{P}{\cos \frac{A}{2}}=\frac{Q}{\cos \frac{B}{2}}=\frac{R}{\cos \frac{C}{2}}\)

B
\(\frac{P}{O A}=\frac{Q}{O B}=\frac{R}{O C}\)

C
\(\frac{P}{\sin \frac{A}{2}}=\frac{Q}{\sin \frac{B}{2}}=\frac{R}{\cos \frac{C}{2}}\)

D
None of these

Solution

From Lamis theorem \(\frac{P}{\sin (\pi-(B+C) / 2)}=\frac{Q}{\sin (\pi-(A+C) / 2)}=\frac{R}{\sin (\pi-(A+B) / 2)} \mathrm{s} 0 \mathrm{P}: Q: \mathrm{R}=\cos \mathrm{A} / 2: \cos\)
\(b / 2: \cos c / 2\)
Question 8
4 / -1

Directions: The following question has four choices out of which ONLY ONE is correct.

Seven conductors each of resistance R are arranged as shown in the figure. (i), fig. (ii) and fig. (iii). If R1, R2and R3are the respective equivalent resistances between A and B, then

A
maximum (R1, R2, R3) = R1

B
R3> R2< R1

C
minimum (R1, R2, R3) = R2

D
R2< R1< R3

Solution
Question 9
4 / -1

A police jeep moving with a velocity of 45 km/hr is chasing a thief in another jeep moving with a velocity of 153 km/hr. The police fire a bullet with muzzle velocity of 180 m/s. The velocity with which it will strike the jeep of the thief is

A
150 m/s

B
27 m/s

C
450 m/s

D
250 m/s

Solution

Velocity of police jeep \(=45 \mathrm{km} / \mathrm{hr}=45 \times 5 / 18=25 / 2 \mathrm{m} / \mathrm{s}\)
Velocity of thief's jeep \(=153 \times 5 / 18=85 / 2 \mathrm{m} / \mathrm{s}\)
Muzzle velocity \(=180 \mathrm{m} / \mathrm{s}\) Velocity of thief's jeep relative to the police jeep \(=85 / 2-25 / 2=60 / 2=30 \mathrm{m} / \mathrm{s}\)
Velocity with which the bullet with muzzle strikes thief's jeep \(=180-30=150 \mathrm{m} / \mathrm{s}\)
Question 10
4 / -1

Let there be four articles having colours blue, red, black and white. When they are heated together and allowed to cool, which article will cool at the earliest?

A
Blue

B
Red

C
Violet

D
White

Solution

Red colour has maximum wavelength.

From Wien's displacement law the relation between maximum wavelength λm and temperature T is

Which implies longer the wavelength smaller the temperature. Since, red colour has maximum wavelength, so its temperature will be minimum and hence, it will cool at the earliest.