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

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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]

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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]

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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

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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%

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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%

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The length, breadth, and thickness of a block are given by l = 12 cm, b = 6 cm and t = 2.45 cm The volume of the block according to the idea of significant figures should be 

(1) 1 × 102 cm3

(2) 2 × 102 cm3

(3) 1.763 × 102 cm3

(4) None of these

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Significant Figures
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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

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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

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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

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