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LEGENDS’ (MGDN) STUDY MA TERIAL =I ee, , , , , , , , , , PUC PHYSICS (NCERT)-Units and Measurer, nents, , On comparing the powers of L, we get,, , x+y=0 > x=-y, , ee ee om (2, = eee |=), , (2)and(3)in(1) > T = Kig 2, , i Ge 2g 7?, , , , , 172, CR ce, a”, , , , , , , , , , For practice |, 1. Assuming that velocity of sound is v in a gas depend upon pressure p and |, , density p of the gas, derive the relation between vy, p and p |, 2. The centripetal acceleration(a) of a particle executing simple harmonic moi, , may depend on i) mass of the particle(m) _ ii) the radius of the circular path(r), (iii)the uniform speed with which the particle is moving(v). Obtain an expression, for acceleration by the method of dimensions., , 3. The excess pressure(p) inside a spherical soap bubble over that out side|, depends upon the radius(r) and the surface tension (1). Obtain an expression for, (p) by the method of dimensions., , 4. The time period (T) of oscillation of glass bubble from an explosion under water, , depends upon static pressure(p) , density of water(p) and total energy of, , explosion(E). Obtain an expression for (1) by the method of dimensions., , ————, , , , , , , NOTE, , , , , , , , , , Limitations of dimensional analysis, , I . . . i Tt,, 1. The dimensional analysis does not give any information about numbers like, , % etc. : : ond trigonometric, 2. It can not be used to study relations involving exponential an, functions. onality constant without, , 3. It can not be used to obtained dimensions of proporti, | knowing its nature. ,, (va It cannot be used to derive relation for a physi, , —, , upon other than length, mass and time., , t depends, , , , cal quantity if