Question
Explain the difference between static friction, kinetic friction and rolling friction.
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Answer
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Figure. shows the position-time graph of a particle of mass 4kg. What is the (a) force on the particle for t < 0, t > 4s, 0 < t < 4s? (b) impulse at t = 0 and t = 4s? (Consider one-dimensional motion only). 
A cylindrical piece of cork of density of base area $A$ and height $h$ floats in a liquid of density $\rho_l$. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period $T=2 \pi \sqrt{\frac{h \rho}{\rho, g}}$ Where $\rho$ is the density of cork. (Ignore damping due to viscosity of the liquid).
→The convex surface of a thin concavo-convex lens of glass of refractive index $1.5$ has a radius of curvature $20cm$. The concave surface has a radius of curvature $60cm$. The convex side is silvered and placed on a horizontal surface as shown in figure.
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A helicopter of mass 2000kg rises with a vertical acceleration of $15m s^{–2}$. The total mass of the crew and passengers is 500kg. Give the magnitude and direction of the $(g = 10m s^{–2})$
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A parallel beam of white light is incident normally on a water film $1.0 \times 10^{-4}cm$ thick. Find the wavelength in the visible range $(400nm - 700nm)$ which are strongly transmitted by the film. Refractive index of water = $1.33$.
→Two ideal gas thermometers A and B use oxygen and hydrogen respectively. The following observations are made:
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Temperature
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Pressure thermometer A
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Pressure thermometer B
|
|
Triple-point of water
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$1.250 \times 10^5Pa$
|
$0.200 \times 10^5Pa$
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Normal melting point of sulphur
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$1.797 \times 10^5Pa$
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$0.287 \times 10^5Pa$
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What do you think is the reason behind the slight difference in answers of thermometers A and B? (The thermometers are not faulty). What further procedure is needed in the experiment to reduce the discrepancy between the two readings?
A $10g$ bullet with a charge of $4.00\mu\text{C}$ is fired at a speed of $270m/s^{-1}$ in a horizontal direction. A vertical magnetic field of $500\mu\text{T}$ exists in the space. Find the deflection of the bullet due to the magnetic field as it travels through 100m. Make appropriate approximations.
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