in aieee 2009 physics..an 8 mrks question was dat....if x,v,a denote displacement vel .and acc. of a partical executing shm of time period T...which will not change wid time?1)a(square)*t(square)+4pi(Square)v(square)2)aT/x3)aT+2pi v4)aT/vthe answer given is 2)but my doubt is ....on checking da dimensions.....option 4) comes out to b constant( ((m/sec.square)*sec)/(m/sec)=1)...hence it should b da answer....right..
Not a blunder. Everything dimensionless need not be a constant.
In, say, free expansion of a gas, you could write an expression for 'n'(number of moles). This would certainly be dimensionless, and with equal certainity, is increasing with time.
There could be any number of such examples if you consider dimensionless quantities like n, strain etc.
So, the answer shown by Nugorama is perfect.
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