A student forgot Newton's formula for speed of sound but the knows there speed (v), pressure (p) and density (d) in the formula. He then start using dimensional analysis method to find the actual relation.
`upsilon = kp^(x)d^(y)`
Where k is a dimensionless constant. On the basis of above passage answer the following questions:
The value of y is :
A student forgot Newton's formula for speed of sound but the knows there speed (v), pressure (p) and density (d) in the formula. He then start using dimensional analysis method to find the actual relation.
`upsilon = kp^(x)d^(y)`
Where k is a dimensionless constant. On the basis of above passage answer the following questions:
The value of y is :
`upsilon = kp^(x)d^(y)`
Where k is a dimensionless constant. On the basis of above passage answer the following questions:
The value of y is :
A
1
B
`(1)/(2)`
C
`-(1)/(2)`
D
2
Text Solution
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The correct Answer is:
C
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A student forgot Newton's formula for speed of sound but the knows there speed (v), pressure (p) and density (d) in the formula. He then start using dimensional analysis method to find the actual relation. upsilon = kp^(x)d^(y) Where k is a dimensionless constant. On the basis of above passage answer the following questions: If the density will increase the speed of sound will :
A student forgot Newton's formula for speed of sound but the knows there speed (v), pressure (p) and density (d) in the formula. He then start using dimensional analysis method to find the actual relation. upsilon = kp^(x)d^(y) Where k is a dimensionless constant. On the basis of above passage answer the following questions: If the density will increase the speed of sound will :
A
increase
B
decrease
C
unchanged
D
none of these
The speed (v) of sound in a gas is given by v = k P^(x) ρy Where K is dimensionless constant, P is pressure, and ρ is the density, then
The speed (v) of sound in a gas is given by v = k P^(x) ρy Where K is dimensionless constant, P is pressure, and ρ is the density, then
A
`x = ½, y = ½`
B
`x = –½, y = –½`
C
`x = ½, y = –½`
D
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The velocity of sound in air (V) pressure (P) and density of air (d) are related as V alpha p^(x) d^(y) . The values of x and y respectively are
The velocity of sound in air (V) pressure (P) and density of air (d) are related as V alpha p^(x) d^(y) . The values of x and y respectively are
A
`1,(1)/(2)`
B
`-(1)/(2),-(1)/(2)`
C
`(1)/(2),(1)/(2)`
D
`(1)/(2),-(1)/(2)`
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A locus is the curve traced out by a point which moves under certain geomatrical conditions: To find the locus of a point first we assume the co-ordinates of the moving point as (h,k) and then try to find a relation between h and k with the help of the given conditions of the problem. If there is any variable involved in the process then we eliminate them. At last we replace h by x and k by y and get the locus of the point which will be an equation in x and y. On the basis of above information, answer the following questions Locus of centroid of the triangle whose vertices are (acost, asint), (bsint,-b cost) and (1, 0) where t is a parameter is -
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The speed of a molecule of a gas changes continuously as a result of collisions with other molecules and with the walls of the container. The speeds of individual molecules therefore change with time. A direct consequence of the distribution of speeds is that the average kinetric energy is constant for a given temperature. The average K.E. is defined as bar(KE) =1/N((1)/(2)m underset(i)SigmadN_(i)u_(1)^(2)) = 1/2 m(underset(i)Sigma(dN_(i))/(N).u_(1)^(2)) where (dN)/(N) is the fraction of molecules having speeds between u_(i) and u_(i) + du and as proposed by maxwell (dN)/(N) = 4pi ((m)/(2pi KT))^(3//2) exp (-("mu"^(2))/(2KT)).u^(2).du The plot of ((1)/(N) (dN)/(du)) is plotted for a particular gas at two different temperature against u as shown. The majority of molecules have speeds which cluster around "v"_("MPS") in the middle of the range of v. There area under the curve between any two speeds V_(1) "and" V_(2) is the fraction of molecules having speeds between V_(1) "and" V_(2). The speed distribution also depends on the mass of the molecules. As the area under the curve is the same (equal to unity) for all gas samples, samples which have the same "V"_("MPS") will have identical Maxwellian plots. On the basis of the above passage answer the questions that follow. For the above graph, drawn for two different samples of gases at two different temperature T_(1) "and" T_(2). Which of the following statements is necessarily true?
The speed of a molecule of a gas changes continuously as a result of collisions with other molecules and with the walls of the container. The speeds of individual molecules therefore change with time. A direct consequence of the distribution of speeds is that the average kinetric energy is constant for a given temperature. The average K.E. is defined as bar(KE) =1/N((1)/(2)m underset(i)SigmadN_(i)u_(1)^(2)) = 1/2 m(underset(i)Sigma(dN_(i))/(N).u_(1)^(2)) where (dN)/(N) is the fraction of molecules having speeds between u_(i) and u_(i) + du and as proposed by maxwell (dN)/(N) = 4pi ((m)/(2pi KT))^(3//2) exp (-("mu"^(2))/(2KT)).u^(2).du The plot of ((1)/(N) (dN)/(du)) is plotted for a particular gas at two different temperature against u as shown. The majority of molecules have speeds which cluster around "v"_("MPS") in the middle of the range of v. There area under the curve between any two speeds V_(1) "and" V_(2) is the fraction of molecules having speeds between V_(1) "and" V_(2). The speed distribution also depends on the mass of the molecules. As the area under the curve is the same (equal to unity) for all gas samples, samples which have the same "V"_("MPS") will have identical Maxwellian plots. On the basis of the above passage answer the questions that follow. If two gases A and B and at temperature T_(A) "and"T_(B) respectivley have identical Maxwellian plots then which of the following statement are true?
The speed of a molecule of a gas changes continuously as a result of collisions with other molecules and with the walls of the container. The speeds of individual molecules therefore change with time. A direct consequence of the distribution of speeds is that the average kinetric energy is constant for a given temperature. The average K.E. is defined as bar(KE) =1/N((1)/(2)m underset(i)SigmadN_(i)u_(1)^(2)) = 1/2 m(underset(i)Sigma(dN_(i))/(N).u_(1)^(2)) where (dN)/(N) is the fraction of molecules having speeds between u_(i) and u_(i) + du and as proposed by maxwell (dN)/(N) = 4pi ((m)/(2pi KT))^(3//2) exp (-("mu"^(2))/(2KT)).u^(2).du The plot of ((1)/(N) (dN)/(du)) is plotted for a particular gas at two different temperature against u as shown. The majority of molecules have speeds which cluster around "v"_("MPS") in the middle of the range of v. There area under the curve between any two speeds V_(1) "and" V_(2) is the fraction of molecules having speeds between V_(1) "and" V_(2). The speed distribution also depends on the mass of the molecules. As the area under the curve is the same (equal to unity) for all gas samples, samples which have the same "V"_("MPS") will have identical Maxwellian plots. On the basis of the above passage answer the questions that follow. If a gas sample contains a total of N molecules. The area under any given maxwellian plot is equal ot :