A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity η flowing per second through a tube of radius r and length l and having a pressure difference p across its end, is

(1) V=πpr48ηl

(2) V=πηl8pr4

(3) V=8pηlπr4

(4) V=πpη8lr4

Subtopic:  Dimensions |
 67%
From NCERT
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The velocity v (in cm/sec) of a particle is given in terms of time t (in sec) by the relation v=at+bt+c; the dimensions of a, b and c are

(1) a=L2,b=T,c=LT2

(2) a=LT2,b=LT,c=L

(3) a=LT2,b=L,c=T

(4) a=L,b=LT,c=T2

Subtopic:  Dimensions |
 83%
From NCERT
PMT - 1990
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From the dimensional consideration, which of the following equation is correct ?

(1) T=2πR3GM

(2) T=2πGMR3

(3) T=2πGMR2

(4) T=2πR2GM

Subtopic:  Dimensions |
 57%
From NCERT
PMT - 1983
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The position of a particle at time t is given by the relation l =voα(1-eαt) , where v0 is a constant and α > 0. The dimensions of v0 and α are respectively

(1) M0L1T1 and T–1

(2) M0L1T0 and T–1

(3) M0L1T1 and LT–2

(4) M0L1T1 and T

Subtopic:  Dimensions |
 71%
From NCERT
PMT - 1995
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The dimensions of ab in the equation P=at2bx, where P is pressure, x is distance and t is time, are 

(1) MT–2

(2) M2LT–3

(3) ML3T–1

(4) LT–3

Subtopic:  Dimensions |
 77%
From NCERT
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Dimensions of 1μ0ε0, where symbols have their usual meaning, are 

(1) [LT–1]

(2) [L–1T]

(3) [L–2T2]

(4) [L2T–2]

Subtopic:  Dimensions |
 58%
From NCERT
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The dimensions of e2/4πε0hc, where e,ε0,h and c are electronic charge, electric permittivity, Planck’s constant and velocity of light in vacuum respectively 

(1) [M0L0T0]

(2) [M1L0T0]

(3) [M0L1T0]

(4) [M0L0T1]

Subtopic:  Dimensions |
 68%
From NCERT
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If radius of the sphere is (5.3 ± 0.1)cm. Then percentage error in its volume will be 

(1) 3+6.01×1005.3

(2) 13×0.01×1005.3

(3) 3×0.15.3×100

(4) 0.15.3×100

Subtopic:  Errors |
 82%
From NCERT
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The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively 4% and 2%. The maximum error in the measurement of pressure is 

(1) 1%

(2) 2%

(3) 6%

(4) 8%

Subtopic:  Errors |
 71%
From NCERT
PMT - 1993
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While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of time period. His percentage error in the measurement of g by the relation g=4π2(l/T2) will be

(1) 2%

(2) 4%

(3) 7%

(4) 10%

Subtopic:  Errors |
 84%
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