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Chapter 10: Problem 82
If \(S\) is stress and \(Y\) is Young's modulus of material of a wire, then the energy stored in the wire per unit volume is (A) \(2 S^{2} Y\) (B) \(S^{2} / 2 Y\) (C) \(2 Y / S^{2}\) (D) \(S / 2 Y\)
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A cubic vessel (with face horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of \(500 \mathrm{~ms}^{-1}\) in vertical direction. The pressure of the gas inside the vessel as observed by us on the ground (A) Remains the same because \(500 \mathrm{~ms}^{-1}\) is very much smaller than \(v_{\mathrm{rms}}\) of the gas. (B) Remains the same because motion of the vessel as a whole does not affect the relative motion of the gas molecules and the walls. (C) Will increase by a factor equal to \(\left(v_{\mathrm{mns}}^{2}+(500)^{2}\right) / v_{\mathrm{mns}}^{2}\), where \(v_{\mathrm{rms}}\) was the original mean square velocity of the gas. (D) Will be different on the top wall and bottom wall of the vessel.
An inflated rubber balloon contains 1 mole of an ideal gas, has a pressure \(p\), volume \(V\), and temperature \(T\). If the temperature rises to \(1.1 T\), and the volume is increased to \(1.05 \mathrm{~V}\), the final pressure will be (A) \(1.1 p\) (B) \(p\) (C) less than \(p\) (D) between \(p\) and \(1.1\)
If spring is disconnected and top part of cylinder is removed, then find the angular frequency for small oscillation. (Assuming pressure of gas at equilibrium position is \(P_{1}\) and length of gas column is \(l_{1}^{-}\)) (A) \(\sqrt{\frac{\gamma P_{1} S_{0}}{m l_{1}}}\) (B) \(\sqrt{\frac{2 \gamma P S_{0}}{m l_{1}}}\) (C) \(\sqrt{\frac{\gamma P_{1} S_{0}}{4 m l_{1}}}\) (D) \(\sqrt{\frac{\gamma P_{1} S_{0}}{2 m l_{1}}}\)
Mark the correct options (A) A system \(X\) is in thermal equilibrium with \(Y\) but not with \(Z\). The system \(Y\) and \(Z\) may be in thermal equilibrium with each other. (B) A system \(X\) is in thermal equilibrium with \(Y\) but not with \(Z\). The system \(Y\) and \(Z\) are not in thermal equilibrium with each other. (C) A system \(X\) is neither in thermal equilibrium with \(Y\) nor with \(Z\). The systems \(Y\) and \(Z\) must be in thermal equilibrium with each other. (D) A system \(X\) is neither in thermal equilibrium with \(Y\) nor with \(Z\). The systems \(Y\) and \(Z\) may be in thermal equilibrium with each other.
A wooden wheel of radius \(R\) is made of two semicircular parts (see Fig. 10.24). The two parts are held together by a ring made of a metal strip of crosssectional area \(S\) and length \(L . L\) is slightly less than \(2 p R\). To fit the ring on the wheel, it is heated so that its temperature rises by \(\Delta T\) and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semi-circular parts together. If the coefficient of linear expansion of the metal is \(a\) and its Young's modulus is \(Y\), then the force that one part of the wheel applies on the other part is (A) \(2 \pi S Y \alpha \Delta T\) (B) \(S Y \alpha \Delta T\) (C) \(\pi S Y \alpha \Delta T\) (D) \(2 S Y \alpha \Delta T\)
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