unit vector and dimensions
The dimension of B?/2uo, where B is magnetic field and
H, is the magnetic permeability of vacuum, is (a)ML:T-?(b)ML-1T-2
(C)MLT-2(d)ML:T-
2.A quantityfis given by f= Jhe1G where c is speed of light, G universal gravitational constant and h is the Plank's constant. Dimension of f is that of
(a) area
(c)momentum
(b) volume
(d) energy
3.The dimension of stopping potential V, in photoelectric ef-fect in units of Planck's constant h', speed of light 'C', Gravi-tational constant 'G' and ampere A is
(b)h°CG'Al
1PeD1-°12-.4(B)
(C) h'G/22!3l 4.If speed V, area A and force F are chosen as fundamental
units, then the dimension of Young's modulus will be
(a) FA-/Yyo (b) FARV-1
(c)FA4V-2(d) FA2V-3
5.If momentum (P), area (4) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is
(a) [PA1T-1
(c)[PAT1
(b)[P4I2TI
(d)[PIZAT-I
6.Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimen-sion of solar constant is
(a) ML.272
(C) MELOT-
(b) ML.T2
(d) ML0T3
7.Dimensional formula for thermal conductivity is (here K
denotes the temperature)
(a)MLT-K
(C)MLT-K-2
(b)MIT-K
(d)MITKI
8.A quantity.xis givenby (IFv?/wL') in terms of momentof inertia I, force F, velocity v, work W and Length L. The di-mensional formula for r is same as that of
(a) Planck's constant (b) Force constant
(c) Energv densitv (d) Coefficient of viscosity
The quantities r=-=,y=s and 2=are defined
CR
where C-capacitance, R-resistance, 1-length, E-Electric field.B-magnetic field and £n, M -free space permittivity and per-meability respectively. Then
(a) Only r and y have the same dimension (b) x, y and z have the same dimension (c) Only r and z have the same dimcnsion (d) Only y and z have the same dimension
10.A simple pendulum is being used to determine the value of gravitional acceleration g at a certain place. The length of the pendulum is 25.0 cm and a stop watch with I s resolution mcasures the time taken for 40 oscillations to be 50 s. The accuracy in g is
(a)2.40%
(c)4.40%
(b)5.40%
(d)3.40%
11. A physical quantity z depends on four observables a, b,
a’62/3
and d, as 2=Jca· The percentagc of error in the me?
surement of a, b, c and d are 2%, 1.5%, 4% and 2.5% respe
tively. The percentage of error in z is
(a)12.25%(b)14.5%
(C)16.5%(d) 13.5%
12. For the four sets of three measured physical quantities as given below, which of the following options is correct?
(i) A=24.36, B,=0.0724, C=256.2(ii) 4, = 24.44, B, =16.082, C, =240.2(i) 4, =25.2, B, =19.2812, C, =236.183(iv) A, =25, B, =236.191, C, =19.5
(a)4+B+G<A+B.+C,=4,+B,+C,<A,+B,+C (b)4+B+C=A+B.+C,=4,+B,+C,=A,+B,+C (c)A, +B +C<A+B,+C<A,+B, +C, <A,+B, +C (d)4,+B,+C<A+B+G<A+B, +C,<A+B.+C
13. Ifthe screw on a screw-gauge is given six rotations, it move by 3 mm on the main scale. If there are 50 divisions on th circular scale the least count of the screw gauge is
(a)0.001 cm (b)0.01cm
(c)0.02mm (d)0.001mm
14. Using screw gauge of pitch 0.I cm and 50 divisions on its circular scale, the thickness of an object is measured. Ii should correctly be recorded as
(a)2.123cm
(C)2.121cm
(b)2.125cm
(d)2.124cm
15. A screw gauge has 50 divisions on its circular scale. Th circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, displacement of 0.5 mm is noticed on the pitch scale. Th nature of zero errorinyolved, and the least count of the screv gauge, are respectively
(a)Negativc, 2um (b) Positive, 10um
(c)Positive. 0.lum (d) Positive, 0.1 mm
16. A student measuring the diameter of a pencilof circular cross section with the help of a vernier scale records the followin four readings 5.50 mm, 5.55 mm, 5.45 mm, 5.65 mm. The aver age of these four readings is 5.5375 mm and the standaro deviation of the data is 0.07395 mm. The average diameter o the pencil should therefore be recorded as
(a) (5.5375±0.0739)mm (b) (5.538±0.074)mm
(c) (5.54±0.07)mm (d)(5.5375±0.0740)mm