An air bubble inside water oscillates due to some explosion with period T. If T P a d b E c then determine the values of a, b and c. Here P, d and E are the static pressure, density and total energy of explosion of water respectively. –
Text Solution
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T ∝ P a d b E c
Pressure [P] = [ML –1 T –2 ]
Density [d] = [ML –3 ]
Energy[E] = [ML 2 T –2 ]
T ∝ [ML –1 T –2 ] a [ML –3 ] b [ML 2 T –2 ] c [M
0 L 0 T 1 ] = [M a + b + c L –a – 3b + 2c T –2a – 2c ]
⇒ a + b + c = 0 ...............(i)
⇒ – a – 3b + 2c = 0...............(ii)
⇒ –2a – 2c = 1 ...............(iii)
and – 2b + 3c = 0 ..............(iv)
put in
a + 
+ c = 0 a = – 
put in
– 2 
– 2c = 1 3c = 1 c = 
a = 
c. = 
= – 
Put c = 
in (c = 
,
b = 
= 
T 
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