Q: The frequency (v) of an oscillating liquid drop may depend upon radius (r) of the drop, density ( ) of liquid and the surface tension (s) of the liquid as : v=r^a ^b s^c. The values of a, b and c resp

aligned & v= r ^ a ^ b s ^ c [v]=[ r ]^ a [ ]^ b [ s ]^ c \\ & [ T ^ -1 ]= [ L ^1 ]^ a [ M ^1 ~L ^ -3 ]^ b [ MLT L ]^ -2 \\ & T ^ -1 = M ^ b + c L ^ a -3 ~b T ^ -2 c \\ & b + c =0, a -3 ~b =0,-2 c =-1 \\ & c = 1 2 , ~b =- 1 2 , a -3 ~b =0 ; \\ & a + 3 2 =0 a =- 3 2 aligned

Question 1

The dimensional formula of latent heat is:

Accepted Answer

Heat, Q = mL where, L = latent heat L = Q m = ML ^2 ~T ^ -2 M = M ^0 ~L ^2 ~T ^ -2

Question 2

The dimensions of coefficient of self inductance are

Accepted Answer

Energy stored in an inductor, U = 1 2 LI ^2 L = 2 U I ^2 [ L ]= [ ML ^2 ~T ^ -2 ] [ A ]^2 = [ ML ^2 ~T ^ -2 ~A ^ -2 ]

Question 3

On a temperature scale ' X '. The boiling point of water is 65^ X and the freezing point is -15^ X . Assume that the X scale is linear. The equivalent temperature corresponding to -95^ X on the Farenh

Accepted Answer

Boiling point of water, = UFP 65^ Freezing point of water, = LFP -15^ X - LFP UFP - LFP = T _ F -32 212-32 -95-(-15) 65-(-15) = T _ F -32 180 -80 80 = T_F-32 180 T_F=-180+32 T _ F =-148^ F

Question 4

The frequency (v) of an oscillating liquid drop may depend upon radius (r) of the drop, density ( ) of liquid and the surface tension (s) of the liquid as : v=r^a ^b s^c. The values of a, b and c resp

Accepted Answer

aligned & v= r ^ a ^ b s ^ c [v]=[ r ]^ a [ ]^ b [ s ]^ c \ & [ T ^ -1 ]= [ L ^1 ]^ a [ M ^1 ~L ^ -3 ]^ b [ MLT L ]^ -2 \ & T ^ -1 = M ^ b + c L ^ a -3 ~b T ^ -2 c \ & b + c =0, a -3 ~b =0,-2 c =-1 \ & c = 1 2 , ~b =- 1 2 , a -3 ~b =0 ; \ & a + 3 2 =0 a =- 3 2 aligned

Question 5

Electric field in a certain region is given by E = ( A x^2 i + B y^3 j ). The SI unit of A and B are:

Accepted Answer

Electric field in a certain region is given by, E = A x^2 i + B y^3 j [ A x ^2 ]= NC ^ -1 [ A ]= Nm ^2 C ^ -1 [ B y ^3 ]= NC ^ -1 [ B ]= Nm ^3 C ^ -1

Question 6

If force (F), length (L) and time (T) are assumed to be fundamental units, then the dimensional formula of the mass will be

Accepted Answer

Let m = KF ^ a L ^ b T ^ c Substituting the dimensions of [ F ]= [ MLT ^ -2 ],[ L ]=[ L ] and [ T ]=[ T ] and comparing both side, we get m = FL ^ -1 ~T ^ 2

Units and Dimensions — Previous Year Questions & Solutions