A car of mass 1000 kg moves on a circular track with a radius of 40 m. If the coefficient of friction is 1.28, the maximum velocity with which the car can be moved is:
1. \(22.4~\text{m/s}\)
2. \(112~\text{m/s}\)
3. \(\frac{0.64\times40}{1000\times100}~\text{m/s}\)
4. \(1000~\text{m/s}\)

Subtopic:  Uniform Circular Motion |
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The escape velocity for the Earth is \(11.2\) km/s. The mass of another planet is \(100\) times the mass of the Earth and its radius is \(4\) times the radius of the earth. The escape velocity for the planet is:
1. \(280\) km/s
2. \(56.0\) km/s
3. \(112\) km/s
4. \(48\) km/s

Subtopic:  Escape velocity |
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Light travels faster in the air than in glass. This is in accordance with:

1. the wave theory of light.
2. the corpuscular theory of light.
3. neither (1) nor (2)
4. both (1) and (2)
Subtopic:  Huygens' Principle |
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The speed of airflow on the upper and lower surfaces of a wing of an aeroplane is \(v_1\) and \(v_2\) respectively. If \(A\) is the cross-section area of the wing and \(\rho\) is the density of air, then the upward lift is:
1. \(\frac12\rho A(v_2-v_2)\)
2. \(\frac12\rho A(v_1+v_2)\)
3. \(\frac12\rho A(v_1~^2-v_2~^2)\)
4. \(\frac12\rho Av_1~^2+v_2~^2\)

 

Subtopic:  Bernoulli's Theorem |
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A body is thrown with a velocity of \(9.8\) m/s making an angle of \(30^\circ\) with the horizontal. It will hit the ground after a time:
1. \(1.5\) s
2. \(1\) s
3. \(3\) s
4. \(2\) s

Subtopic:  Projectile Motion |
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A radioactive element \({ }_{90} \mathrm{X}^{238}\) decays into \({ }_{83} Y^{222}\). The number of \(\beta\)-particles emitted are:
1. 1
2. 2
3. 4
4. 6

Subtopic:  Types of Decay |
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The minimum excitation potential of Bohr's first orbit in a hydrogen atom is:
1. \(3.6\) V
2. \(10.2\) V
3. \(13.6\) V
4. \(3.4\) V
Subtopic:  Bohr's Model of Atom |
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A gas expands \(0.25~\mathrm{m^3}\) at constant pressure \(10^3~\mathrm{N/m^2}\), the work done is:
1. \(250~\mathrm{N}\) 
2. \(250~\mathrm{W}\) 
3. \(250~\mathrm{J}\) 
4. \(2.5~\mathrm{erg}\) 

Subtopic:  Work Done by a Gas |
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The work done in increasing the size of a soap film for \(10~ \mathrm{cm} \times 6~ \mathrm{m}\) to \(10~ \mathrm{cm} \times 11~ \mathrm{m}\) is \(3\times 10^{-4}\) J. The surface tension of the film is:
1. \(1.0 \times10^{-2}\) N/m
2. \(6.0 \times 10^{-2}\) N/m
3. \(3.0 \times 10^{-2}\) N/m
4. \(1.5 \times 10^{-2}\) N/m

 

Subtopic:  Surface Tension |
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A parallel plate condenser is filled with two dielectrics as shown in the figure. The area of each plate is \(A~\text m^2\) and the separation is \(d\) meter. The dielectric constants are \(K_1\) and \(K_2\) respectively. Its capacitance in farad will be: 
             

1. \(\frac{2\varepsilon_{_0}A}{d}\Big(\frac{K_1+K_2}{K_1K_2}\Big)\)
2. \(\frac{2\varepsilon_{_0}A}{d}\Big(\frac{K_1K_2}{K_1+K_2}\Big)\)
3. \(\frac{\varepsilon_{_0}A}{d}\Big(\frac{K_1+K_2}{2K_1K_2}\Big)\)
4. \(\frac{\varepsilon_{_0}AK_1K_2}{2(d_2K_1+d_1K_2)}\)

 

Subtopic:  Dielectrics in Capacitors |
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