Physics Test

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Physics Test - 4

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Question 1
3 / -1

An 80 kg man standing on ice throws a 4 kg body horizontally at 6 ms⁻¹. The frictional coefficient between the ice and his feet is 0.02. The distance through which the man slips is (g = 10 ms⁻²).

A
0.225 m

B
2.25 m

C
0.115 m

D
0.20 m

Solution
Question 2
3 / -1

If two conducting spheres are separately charged and then brought in contact:

A
The total energy of the two spheres is conserved

B
The total charge on the spheres is conserved

C
Both the total energy and charge are conserved

D
The final potential is always the mean of the original potential of the two spheres

Solution

If two conducting spheres are separately charged and then brought in contact the total charge on the spheres is conserved.
The total charge on the two spheres will be conserved by the law of charge conservation. But energy may not conserve because if they are of a different size or have a different charge then some of their energy might lose in the redistribution of charge. In the case of the final potential, it is not always the mean of original potential because during the redistribution of charge some losses occur, but final potential on both spheres is always equal. People mistakenly think that an object gets a positive charge by receiving extra positive charges, it losses negative charge (electrons) to become positive.
Question 3
3 / -1

A satellite orbiting around the earth of radius R is shifted to an orbit of radius 2R. The time taken for one revolution will increase nearly by

A
2 times

B
2.5 times

C
2.8 times

D
3.2 times

Solution
Question 4
3 / -1

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

For He \(+\), transition is from \(n=3\) to \(n=1\) Energy emitted

\(=E_{2}-E_{1}=4 \times(13.6-3.4)=40.8 e V\)

Work function

\(=\frac{h c}{\lambda_{0}}=\frac{2 \times 10^{-25}}{6000 \times 10^{-10}}(J)=2.3 \mathrm{eV} .\)

The maximum K.E. of electron \(=40.8-2.3=38.5 \mathrm{eV}\)

Stopping potential \(=38.5 V\)

According to the de-Broglie concept of matter waves, the wavelength associated with electron will be,

\(x=\frac{h}{\sqrt{2 m e V}}=\frac{12.27}{\sqrt{V}}=\frac{12.27}{\sqrt{38.5}}=2.0 A^{\circ}\)

The time interval between the incidence of photon and the ejection of the photoelectron is approximately

\(10^{-10}\) seconds, which is an instantaneous process.

Hence option D is the correct answer.
Question 5
3 / -1

Lights of wavelengths \(2000 A^{0}\) and \(3000 A^{0}\) emit photoelectrons from a metal surface whose threshold wavelength is \(4000 A^{0} .\) The ratio of the maximum \(\mathrm{K} . \mathrm{E}\) 's of the photoelectrons emitted is nearly:

A
1:3

B
3:1

C
6:1

D
2:1

Solution
Question 6
3 / -1

A battery of internal resistance 4 Ω is connected to the network of resistance as shown in the Figure. In order to get maximum power to the network, the value of R in ohm should be ?

A
1 Ω

B
1.5 Ω

C
2 Ω

D
2.5Ω

Solution
Question 7
3 / -1

A spring mass system with unequal masses is placed at rest on a smooth horizontal surface. The spring is initially kept compressed with a thread. When the spring is cut, the mass m moves so as to enter in a vertical circular loop of radius r. The minimum compression x in the spring so that the mass m may negotiate the vertical loop is

A

B

C

D

Solution
Question 8
3 / -1

A point mass 0.1 kg executes S.H.M of amplitude 0.2 m. When the particle passes through the mean position, its kinetic energy is 9 × 10^{− 3} J. The equation of motion of their particle is S.H.M when the initial phase 60 ° is

A

B

C

D

Solution
Question 9
3 / -1

An object is projected up the incline with a velocity of 24 m/s at angle of 30 ° as shown in the Figure. The distance up the inclined plane at which the object strikes is (g = 10 ms ^{− 2} )

A
32.6 m

B
34.2 m

C
36.4 m

D
38.4 m

Solution
Question 10
3 / -1

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 = 2.1x10^-3 cal/g (^oC)³; B = 15x10^-2 cal/g (^oC)²].

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

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

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

D
All are correct

Solution

Amount of heat required to change temperature of 'm' gm of a substance by dT \(d Q=m c d T=m\left(A T^{2}+B T\right) d T\)

On integrating between the given limits, the amount of heat required, \(Q=m \int_{320}^{350}\left(A T^{2}+E T\right) d T=m\left[\frac{A T^{3}}{3}+\frac{B T^{2}}{2}\right]_{320}^{950}\)

\(=100\left[\frac{2.1 \times 10^{-3}}{3}\left(350^{3}-320^{3}\right)+7.5 \times 10^{-2}\left(350^{2}-320^{2}\right)\right]\)

\(Q_{2}=858240 \mathrm{cal}=3604608 J\)

Let 't' be the required time; then \(\frac{V^{2} t}{R}=Q\)

or \(t=\frac{Q R}{V^{2}}=\frac{3604608 \times 300}{200 \times 200} \mathrm{sec}=7.5 \mathrm{hr}\)

Hence option D is the correct answer.
Question 11
3 / -1

An electron makes transition from n=4 to n=1 state in a hydrogen atom. The maximum possible number of photons emitted will be :

A
1

B
2

C
3

D
6

Solution

From the nth state, the electron may go to \((n-1)^{t h}\) state, \(\ldots, 2\) nd state or 1 st state. So there are \((n 1)\) possible transitions starting from the \(n^{t h}\) state. The atoms reaching \((n-1)^{t h}\) state may make (n 2) different transitions. The atoms reaching \((n-2)^{t h}\) state may make \((n 3)\) different transitions. Similarly for other lower states. During each transition a photon with energy \(h \nu\) and wavelength \(\lambda\) is emitted out. Hence, the total number of possible transitions is equal to the number of photons emitted. The total number of possible transitions is \((n-1),(n-2),(n-3), \ldots \ldots \ldots \ldots \ldots \ldots, 3,2,1=\frac{n(n-1)}{2}\)
Therefore, for transition of an electron from higher energy state \(n=4\) to lower energy state \(n=1\) the number of photons emitted are \(\frac{n(n-1)}{2}=\frac{4(4-1)}{2}=\frac{12}{2}=6\)
Hence only option D is the correct answer.
Question 12
3 / -1

The beat frequency produced when the following two waves x₁ = 12 sin (484 π t − 7π x) and x₂= 12 sin (480 πt − 7π x) are sounded together is

A
4

B
3

C
2

D
1

Solution
Question 13
3 / -1

Steam at 100 °C is passed into 1.4 kg of water kept in a calorimeter of water equivalent 0.03 kg at 20 °C till the temperature of the calorimeter and contents reach 80 °C. Latent heat of steam is 2.26 × 106 J kg ^{− 1} and sp.heat capacity of water is 4200 J /kg/ °C. The mass of steam condensed in kilogram is nearly equal to

A
0.15 kg

B
0.16 kg

C
0.18 kg

D
0.18 kg

Solution
Question 14
3 / -1

The given graph shows the extension ( Δl ) of a wire of length 1.0 m suspended from the top of a roof at one end and loaded at the other end. If the cross sectional area of the wire is 10 ⁻6 m², the Young’s modulus Y of the material of the wire is ?

A
2 × 10 ^{− 7}Nm ^{− 2}

B
3 × 10⁷ Nm^{− 2}

C
2 × 10¹¹ Nm ^{− 2}

D
2 × 10⁹ Nm ^{− 2}

Solution
Question 15
3 / -1

Four metallic plates each with a surface area A of each side are placed at a distance d from each other. When the plates are connected as shown in Figure, the capacitance of the whole system between a and b is

A

B

C

D

Solution

The equivalent of the qiven arrangement is shown below

Hence option A is the correct answer.