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The potential energy of a particle falling through a straight shaft drilled through the earth (assumed homogenous and spherical) is proportional to (where r is the distance of’the particle from centre of the earth)

The potential energy of a particle falling through a straight shaft drilled through the earth (assumed homogenous and spherical) is proportional to (where r is the distance of’the particle from centre of the earth) Correct Answer r<sup>2</sup>

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From the following data, calculate the critical speed of the shaft in rps. Shaft diameter = 5mm length = 200mm Mass of disc = 50Kg at centre of shaft E = 200GN/m2 Centre of disc at 0.25m away from centre of axis of shaft.
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Read the passage carefully and choose the best answer to each question out of the four alternatives and click the button corresponding to it.
Modern civilization is completely dependent on energy, which has therefore to be abundant and also economical. About 85% of the world's energy is supplied by oil, coal and natural gas while nuclear, hydro, wind and solar power and biomass supply the rest. Coal, nuclear and hydro are used primarily to generate electricity while natural gas is widely used for heating. Biomass is used both for heating and cooking. The wind and solar power is the future's hope as they are sustainable energy sources. Oil powers almost all machines that move and that makes oil uniquely versatile. Oil powered airplanes carry 500 people across the widest oceans at nearly the speed of sound. Oil powered machines produce and transport food. Oil powered machines are ubiquitous. Clearly, we live in the age of oil but it is drawing to a close. According to data available if oil production remains constant until it's gone, there is enough to last 42 years. Oil wells will produce less as they become depleted, which will make it impossible to keep production constant. Similarly natural gas and coal will last another 61 years and 133 years respectively. Naturally, as they become scarce, they become expensive, leading to a worldwide energy crisis. If we are to survive on this planet, we have to make a transition to sustainable energy sources. The transition may be willy-nilly or planned - the choice is ours. The dawning era of limited and expensive energy will be very difficult for everyone on earth but will be even more difficult if it is not anticipated. It is of utmost importance that the public and policymakers understand the global energy crisis and act in tandem to ensure that the species 'homo sapiens' does not become extinct. Biomass is an energy source used in
Read the passage carefully and choose the best answer to each question out of the four alternatives and click the button corresponding to it.
Modern civilisation is completely dependent on energy, which has therefore to be abundant and also economical. About 85% of the world's energy is supplied by oil, coal and natural gas while nuclear, hydro, wind and solar power and biomass supply the rest. Coal, nuclear and hydro are used primarily to generate electricity while natural gas is widely used for heating. Biomass is used both for heating and cooking. The wind and solar power is the future's hope as they are sustainable energy sources. Oil powers almost all machines that move and that makes oil uniquely versatile. Oil powered airplanes carry 500 people across the widest oceans at nearly the speed of sound. Oil powered machines produce and transport food. Oil powered machines are ubiquitous. Clearly, we live in the age of oil but it is drawing to a close. According to data available if oil production remains constant until it's gone, there is enough to last 42 years. Oil wells will produce less as they become depleted, which will make it impossible to keep production constant. Similarly natural gas and coal will last another 61 years and 133 years respectively. Naturally, as they become scarce, they become expensive, leading to a worldwide energy crisis. If we are to survive on this planet, we have to make a transition to sustainable energy sources. The transition may be willy-nilly or planned - the choice is ours. The dawning era of limited and expensive energy will be very difficult for everyone on earth but will be even more difficult if it is not anticipated. It is of utmost importance that the public and policymakers understand the global energy crisis and act in tandem to ensure that the species 'homo sapiens' does not become extinct. The energy sources of the future are
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A double universal joint is used to connect two shafts in the same plane. The intermediate shaft is inclined at an angle of 20° to the driving shaft as well as the driven shaft. Find the minimum speed of the intermediate shaft if the driving shaft has a constant speed of 500 r.p.m.