Physics-
General
Easy

Question

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d subscript 1 end subscript and d subscript 2 end subscript are filled in the tube. Each liquid subtends 90 to the power of ring operator end exponent angle at centre. Radius joining their interface makes an angle alpha with vertical. ratio d subscript 1 end subscript divided by d subscript 2 end subscript is

  1. fraction numerator 1 plus t a n invisible function application alpha over denominator 1 minus t a n invisible function application alpha end fraction    
  2. fraction numerator 1 plus s i n invisible function application alpha over denominator 1 minus c o s invisible function application alpha end fraction    
  3. fraction numerator 1 plus s i n invisible function application alpha over denominator 1 minus s i n invisible function application alpha end fraction    
  4. fraction numerator 1 plus cos invisible function application alpha over denominator 1 minus cos invisible function application alpha end fraction    

The correct answer is: fraction numerator 1 plus t a n invisible function application alpha over denominator 1 minus t a n invisible function application alpha end fraction

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When jet of liquid strikes a fixed or moving surface, it exerts thrust on it due to rate of change of momentum. F = open parentheses rho A v subscript 0 end subscript close parentheses v subscript 0 end subscript minus open parentheses rho A v subscript 0 end subscript close parentheses v subscript 0 end subscript c o s invisible function application theta equals rho A v subscript 0 end subscript superscript 2 end superscript left square bracket 1 minus c o s invisible function application theta right square bracket

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Based on above concept, in the below given figure, if the cart is frictionless and free to move in horizontal direction, then answer the following :Given cross–section area of jet equals 2 cross times 10 to the power of negative 4 end exponent m to the power of 2 end exponent velocity of jet V subscript 0 end subscript = 10 m/s, density of liquid = 1000 kg/ m to the power of 3 end exponent , Mass of cart M = 10 kg: The power supplied to the cart, when its velocity becomes 5 m/s, is equal to :

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If surface is free and starts moving due to thrust of liquid, then at any instant, the above equation gets modified based on relative change of momentum with respect to surface. Let any instant the velocity of surface is u, then above equation becomes – F equals rho A open parentheses v subscript 0 end subscript minus u close parentheses to the power of 2 end exponent left square bracket 1 minus c o s invisible function application theta right square bracket

Based on above concept, in the below given figure, if the cart is frictionless and free to move in horizontal direction, then answer the following :Given cross–section area of jet equals 2 cross times 10 to the power of negative 4 end exponent m to the power of 2 end exponent velocity of jet V subscript 0 end subscript = 10 m/s, density of liquid = 1000 kg/ m to the power of 3 end exponent , Mass of cart M = 10 kg: The time at which velocity of cart becomes 2m/s, is equal to:

When jet of liquid strikes a fixed or moving surface, it exerts thrust on it due to rate of change of momentum. F = open parentheses rho A v subscript 0 end subscript close parentheses v subscript 0 end subscript minus open parentheses rho A v subscript 0 end subscript close parentheses v subscript 0 end subscript c o s invisible function application theta equals rho A v subscript 0 end subscript superscript 2 end superscript left square bracket 1 minus c o s invisible function application theta right square bracket

If surface is free and starts moving due to thrust of liquid, then at any instant, the above equation gets modified based on relative change of momentum with respect to surface. Let any instant the velocity of surface is u, then above equation becomes – F equals rho A open parentheses v subscript 0 end subscript minus u close parentheses to the power of 2 end exponent left square bracket 1 minus c o s invisible function application theta right square bracket

Based on above concept, in the below given figure, if the cart is frictionless and free to move in horizontal direction, then answer the following :Given cross–section area of jet equals 2 cross times 10 to the power of negative 4 end exponent m to the power of 2 end exponent velocity of jet V subscript 0 end subscript = 10 m/s, density of liquid = 1000 kg/ m to the power of 3 end exponent , Mass of cart M = 10 kg: The time at which velocity of cart becomes 2m/s, is equal to:

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