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Calculate the total torque acting on the body shown in the following figure about the point O.

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A cubical block of mass m and edge a slides down a rough inclined plane of inclination θ with a uniform speed. Find the torque of the normal force acting on the block about its centre.
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A flywheel of moment of inertia 5⋅0 kg-m2 is rotated at a speed of 60 rad/s. Because of the friction at the axle it comes to rest in 5⋅0 minutes. Find (a) the average torque of the friction (b) the total work done by the friction and (c) the angular momentum of the wheel 1 minute before it stops rotating.
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A 6⋅5 m long ladder rests against a vertical wall reaching a height of 6⋅0 m. A 60 kg man stands half way up the ladder.
- Find the torque of the force exerted by the man on the ladder about the upper end of the ladder.
- Assuming the weight of the ladder to be negligible as compared to the man and assuming the wall to be smooth, find the force exerted by the ground on the ladder.
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Bernoulli's theorem is based on the conservation of
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Water is flowing through a long horizontal tube. Let PA and PB be the pressures at two points A and B of the tube.
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A large cylindrical tank has a hole of area A at its bottom. Water is poured in the tank by a tube of equal cross-sectional area A ejecting water at the speed v.
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A steel plate of face area 4 cm2 and thickness 0.5 cm is fixed rigidly at the lower surface. A tangential force of 10 N is applied on the upper surface. Find the lateral displacement of the upper surface with respect to the lower surface. Rigidity modulus of steel = 8.4 × 1010 N m−2.
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Suppose the tube in the previous problem is kept vertical with A upward but the other conditions remain the same. the separation between the cross sections at A and B is 15/16 cm. Repeat parts (a), (b) and (c) of the previous problem. Take g = 10 m/s2.
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Suppose the tube in the previous problem is kept vertical with B upward. Water enters through B at the rate of 1 cm3/s. Repeat parts (a), (b) and (c). Note that the speed decreases as the water falls down.
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Four cylinders contain equal number of moles of argon, hydrogen, nitrogen and carbon dioxide at the same temperature. The energy is minimum in
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Show that the internal energy of the air (treated as an ideal gas) contained in a room remains constant as the temperature changes between day and night. Assume that the atmospheric pressure around remains constant and the air in the room maintains this pressure by communicating with the surrounding through the windows, doors, etc.
Use R = 8.314 J K-1 mol-1
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A metal block of heat capacity 80 J°C−1 placed in a room at 20°C is heated electrically. The heater is switched off when the temperature reaches 30°C. The temperature of the block rises at the rate of 2°C s−1 just after the heater is switched on and falls at the rate of 0.2°C s−1 just after the heater is switched off. Assume Newton's law of cooling to hold.
- Find the power of the heater.
- Find the power radiated by the block just after the heater is switched off.
- Find the power radiated by the block when the temperature of the block is 25°C.
- Assuming that the power radiated at 25°C represents the average value in the heating process, find the time for which the heater was kept on.
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State the law of equipartition of energy and hence calculate the molar specific heat of mono-atomic and di-atomic gases at constant volume and constant pressure.
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If universal gas constant is 8.3 joule/mole-Kand the Avogadro's number is 6 x 1023, then mean kinetic energy of the oxygen molecules at 427 °C will be ______.
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Answer the following question based on the P-T phase diagram of carbon dioxide:
At what temperature and pressure can the solid, liquid and vapour phases of CO2 co-exist in equilibrium?
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Answer the following question based on the P-T phase diagram of carbon dioxide:
What is the effect of decrease of pressure on the fusion and boiling point of CO2?
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Answer the following question based on the P-T phase diagram of carbon dioxide:
What are the critical temperature and pressure for CO2? What is their significance?
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Which of the following ratios express pressure?
- Force/Area
- Energy/Volume
- Energy/Area
- Force/ Volume
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There are three forces F1, F2 and F3 acting on a body, all acting on a point P on the body. The body is found to move with uniform speed.
- Show that the forces are coplanar.
- Show that the torque acting on the body about any point due to these three forces is zero.
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