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1.

Find the dimensions of a. linear momentum b. frequency and c. pressure

Answer» Correct Answer - A::B::C
Linear momentum : (a) `mv=[MLT^-1]`
(b) Frequency : `1/T=[M^0 L^0 T(-1)]`
(c) Pressure : `Force/Area = (MLT^(-2)]/(L^2]`
Discussion
2.

If velocity,time and force were chosen as basic quantities, find the dimensions of mass.

Answer» `DimensioN/Ally , Forcer= massxx acceleration `
` =massxx velocity/time`
` mass=(forcexxtime)/velocity`
`[mass]=FTV^-1`
Discussion
3.

The heat produced in a wire carrying an electric current depends on the current, the resistance and the time. Assuming that the dependuance is of the product of powers type, guress an eqn. between these quantites uning dimesional analysis. The dimensional formula of resistance is `ML^2 A^(-2) T^(-3)` and heat is a form of energy.

Answer» Let the heat produced be H, the current through the wire be I, the resistnce be R and the time be t. Since heat is a form of energy, its dimensioN/Al formula is `ML^3T^-2`.
Let us assume that the required equation is
`h=kI^aR^bt^c`,
whre k is a dimensionless constant.
Writing dimension of both sides,
`ML^2T^_2=I^a(ML^2I^-2T^-3)^bT^c`
` =M^bL^(2b)T^(-3b+c)I^(a-2b)`
Equating the exponents,
`b=1`
`2b=2`
` -3b+c=0`
` a-2b=0` Soving these, we get `a=2, b1 and c=1`.
` Thus, the required equation is `H=kl^2 Rt.`
Discussion
4.

The kinetic energy K of a rotating body depends on its moment of inertia I and its angular speed `omega`. Assuming the relation to be `K=kI^(alpha) omega^b` where k is a dimensionless constatnt, find a and b. Moment of inertia of a spere about its diameter is `2/5Mr^2`.

Answer» Correct Answer - A::B
`K=KI^aomega^b
where K=` kinetic energy of rotating body and kk= dimensionless constant Dimensions of left side are `K=[ML^2T^-2]`Dimensions of right side are `I^a=[ML^2}^a, omega^b=[T^-1]^b`
According to principle of homogeneity of dimension
`[ML^2T^-2]=[ML^2][T^-1]^b` Equatin the dimensions of both sides wer get `2=2a and -2=-b
alpha =1 and b=2`
Discussion
5.

The surface tension of water is 72 dyne//cm. convert it inSI unit.

Answer» Correct Answer - B
Surface tension of water ` 72 dyne/cm is` S.I. unit, `72 dyne/cm (72xx10^-5)/(10^-2) N/mltbrge 72xx10^-3 N/m
= 0.72 N/m`
Discussion
6.

The height of mercury column in a barometer in a Calcutta laboratory was recorded to be 75 cm. Calculate this pressure in SI and CGS units the following data, Specific gravity of mercury = 13.6, Density of `water = 10^3 kg/m^3, g=9.8 m/s^2` at Calcutta. Pressure `=h rho g` in usual symbols.

Answer» Correct Answer - A::B::C::D
Height, `h= 75cm = 0.75m` Density of mercury `= 13600 kg/m^3` `g= 9.8 m/sec^2` Pressure `= hrhog` `= (0.75) xx 13600 xx 9.8 = 10 xx 10^4 N/m^2` (approximetely) In C.G.S. units `P= 10 xx 10^4 N/m^2 = (10 xx 10^4 xx 10^5 dyne)/(10^4 cm^2) = 10 xx 10^5 dyne/cm^2`
Discussion
7.

Theory of reltivity reveals that mass can be converted into energy. The energy E so obtained is proportional to certain powers of mass m and the speed c of light. Guess a relation among the quantities using the method of dimensions.

Answer» Correct Answer - B::C
Let Energy `E alpha M^aC^b, where, M=Mass, C=speed of light rarr E= KM^aC^b`
Where K= PrroprtioN/Ality constant Dimension of left side `E=[ML^2T^-2]` Dimension of right side `M^aC^b, = M^a[LT^-1]^b, [ML^2T^-2]=[Ma][LT^-1]^b
rarra=1
b=2`
So, the relation is `E=KMC^2`
Discussion
8.

Express the power of a 100 wtt bulb in CGS unit.

Answer» Correct Answer - A
In S.I. unit 100 watt = 100 joule/sec
In C.G.S. unit `= (100 xx 10^7 dyne)/(1 sec)` `= 10^9` erg/sec (cgs unit)
Discussion
9.

The normal duratioin of I.Sc. Physics practical period in Indian colleges is 100 minute. Express this perod in microcenturies. 1 microcentruy `=10^-6xx100` years. How many microcenturies did you sleep yesterday?

Answer» Correct Answer - A::C
1 micro century `= 10^-5 xx 100` years `=10^-4 xx 365 xx 24 xx 60 min` `100 min = 1/(10^-4 xx 365 xx 24 xx 60) xx 100 = 10^5/(365 xx 144)` `=1.9` microcenturies
Discussion
10.

Suppose a quantilty x can be dimensionally represented in terms of M,L and T, that is `[x], M^aL^bT^c`. The quantity massA. can always be dimensionally represented in terms of L, T and xB. can never be dimensionally represented in terms of L, T and x.C. May be represented in terms of L, T and x if `a!=0`D. does not exist

Answer» Correct Answer - D
Discussion