Question
Describe some day to day activities based on surface tension.
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Answer
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Describe surface tension on the basis of molecular forces.
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There are three forces $F_1, F_2$ and $F_3$ acting on a body, all acting on a point P on the body. The body is found to move with uniform speed.
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A cylinder fitted with a movable piston contains hydrogen at a pressure of $3.5 \times 10^5 \mathrm{~N}-\mathrm{m}^2$ and temperature 366 K . Hydrogen expands adiabatically until the pressure in the cylinder falls to $0.7 \times 10^5 \mathrm{~N}-\mathrm{m}^{-2}$. The piston is then fixed and the gas is heated until the temperature becomes 366 K . The pressure in the cylinder is now found to be $1.1 \times$ $10^5 \mathrm{~N}-\mathrm{m}^{-2}$. Determine the specific heats of hydrogen. $\left(R=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right)$.
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A $100kg$ gun fires a ball of $1kg$ horizontally from a cliff of height $500m$. It falls on the ground at a distance of $400m$ from the bottom of the cliff. Find the recoil velocity of the gun. (acceleration due to gravity $= 10m s^{–2}$)
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An iron bar $\left(L_1=0.1 m , A_1=\right. \left.0.02 m ^2, K_1=79 W m ^{-1} K ^{-1}\right)$ and a brass bar $\left(L_2=0.1 m , A_2=0.02 m ^2\right.$, $K_2=109 W m ^{-1} K ^{-1}$ ) are soldered end to end as shown in Fig. $10.16.$ The free ends of the iron bar and brass bar are maintained at $373 K$ and $273 K$ respectively. Obtain expressions for and hence compute $(i)$ the temperature of the junction of the two bars, $(ii)$ the equivalent thermal conductivity of the compound bar, and $(iii)$ the heat current through the compound bar.
→A block of mass M is moving with a velocity $v_1$ on a frictionless surface as shown in fig. It passes over to a cylinder of radius R and moment of inertia I which has fixed axis and is initially at rest. When it first makes contact with the cylinder, it slips on the cylinder, but the friction is large enough so that slipping ceases before it losses contact with the cylinder. Finally it goes to the dotted position with velocity $v_2$ compute $v_2$ in terms of $v_1, M, I$ and $R$.
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