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A gas bubble from an explosion under water oscillates with a period proportional to P^(a)d^(b)E^(c), where P is the static pressure, d is the density of water and E is the energy of explosion. Then a,b,c are respectively : |
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Answer» `1,1,1` Writing dimensions on both SIDES, `[M^(0)L^(0)T^(0)]=[ML^(-1)T^(-2)]^(a)[ML^(-3)]^(b)[ML^(2)T^(-2)]^(c)` `:.[M^(0)L^(0)T]=M^(a+b+c)L^(-a_3b+2c)T^(-2a-2c)` Thus `a+b+c=0,-a-3b+2c=0,-2a-2c=0.` On solving eqns, we GET `a=(-5)/(6),b=(1)/(2)` and `c=(1)/(3)` Hence the correct `(c )`. |
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