Download Physics CH-1

Units and Measurement
Choose the correct answer :
1.
2.
3.
4.
5.
6.
7.
Find the unit of thermal conductivity K.
(1)
Joule  metre
time  temp
(2)
Joule
time  metre  temp
(3)
Joule  time
metre  temp
(4)
Joule  temp
time  metre
Find the dimensional formula for coefficint of viscosity x.
(1)
MLT 1
(2)
ML2T 1
(3)
ML1T 1
(4)
ML2T
Evaluate
(1)
1038
(2)
1039
(3)
1040
(4)
1041
What are the dimensions of the ratio of angular to linear momentum
(1)
[M0LT0]
(2)
[MLT–1]
(3)
[ML2T–1]
(4)
[M–1L–1T–1]
If the percentage error in calculation of area of a cube is 4 then find the percentage error in calculateing
the volume of cube
(1)
6
(2)
8
3
(3)
8
(4)
4
Choose correctly the dimensional formula for
L
R 2C
(symbols have their usual meaning)
(1)
[M0L0T]
(2)
[M0L0T2]
(3)
[M0L0T0]
(4)
None of these
Find the dimensions of Y, if y 
(1)
8.
25.5  1374
. All ditis in this expression are significant
33.3
Resistance
t
where t is time, L is length, V is potential and e0 is permittivity:
 0LV
(2)
(Current)–1
(3)
(Voltage)–1
(4)
Charge
What will be 1 Joule if, a new system of unit is chosen in which the unit of mass is taken as 10 kg, unit
of length is taken as 1 m and unit of time is taken 10 second.
(1)
1
(2)
1000
(3)
10
(4)
1
10
9.
10.
Which of the following relations cannot be deduced using dimensional analysis?
a.
y = Asin(wt + kx)
b.
K
c.
N = N0e–lt
(1)
(3)
a only
a, b and c
1 2
I  mgh
2
(2)
(4)
Find the dimensional formula for
a and b
c only
Dx
(t  time) if the number of particles crossing per unit volume
t
perpendicular to x-axis per unit time is given by N = D(N2 – N1) (x2 – x1) where N2 and N1 are number
of particles per unit area at x2 and x1 respectively,
11.
12.
(1)
[M0L2T–1]
(2)
[M0L–2T1]
(3)
[M0L–1T–2]
(4)
[M0L–1T0]
Find the dimensional formula for  2V03 if the position of a particle at time t is given by the relation
x
v0
(1  C  t ) .

(1)
[L3T–4]
(2)
[L3T–5]
(3)
[LT–2]
(4)
[L2T–3]
What is the maximum % error in energy stored (E), if energy stored (E) in capacitor is
Q2
, where C
2C
is capacitance and Q is charge on it and error in measurement of C and Q are 1% and 0.5%.
13.
(1)
2
(2)
2.5
(3)
1.5
(4)
0.5
Find the dimensional formula of

. If is given that

in the relation P   e

 z
k
, P is pressure. z is
distance, k is Boltzman’s constant and  is temperature.
14.
15.
(1)
[ML–1T–2]
(2)
[M0L2T0]
(3)
[M0L2T–1]
(4)
[ML2T–1]
A quantity x is defined by the equation x = 3CB2 where C is capacitance and B is magnetic field, then
dimension of x are
(1)
[ML–2]
(2)
[ML–2T–2A]
(3)
[ML–2T–2 A2]
(4)
[L–1A–1]
Caluclate the max % error in increasing the quantity. Dimensional formula of a physical quantity is
[M–1L3T–2]. The errors in measuring quantities M, L and T respectively are 2%, 3% and 4%.
(1)
9
(2)
10
(3)
14
(4)
19
16.
17.
18.
19.
20.
Displacement of particle in nth second moving in straight line is given by Sn = u + a(2n – 1). This
equation is
(1)
Numerically correct only
(2)
Dimensionally correct only
(3)
Both numerically and dimensionally correct
(4)
Neither numerically nor dimensionally correct
The volume V of water passing any point of a uniform tube during t seconds is related to the crosssectional area of the tube (A) and velocity of water (v) and given by V µAavbtc, then which of the
following will be true?
(1)
a=b=c
(2)
a¹b=c
(3)
a=b¹c
(4)
a¹b¹c
Choose the incorrect statement
(1)
0.0037218 has five significant digits
(2)
4.3500 has three significant digits
(3)
1560 has three significant digits
(4)
7.650 has four significant digits
Find the dimension of
23.
. If F = ax + bt2 + c where F is force, x is distance and t is time. ?
[M L2 T–2]
(2)
[M L T–2]
(3)
[M0 L0 T0]
(4)
[M L T–1]
Find which of the following is dimensionless here
µ0 = permeability
e0= permittivity
B = magnetic field
E = electric field
(3)
22.
bt 2
(1)
(1)
21.
axc
 00
E2
B2
E2
0 0B 2
(2)
(4)
0E 2
0B 2
0E 2
 0B 2
Find the dimensional formula of energy if force, time and velocity are treated as fundamental quantities
(1)
[FTV]
(2)
[FT2V]
(3)
[FTV2]
(4)
[FT2V2]
Find the magnitude of 1 N force in new system of units if in a new system of units, unit of mass is 10
kg, unit of length is 100 m, unit of time is 1 minutes.
(1)
36
(2)
60
(3)
3.6
(4)
0.06
Find the error in calculation of surface area of sphere if error in measurement of volume of sphere is
1%.
(1)
2
%
3
(2)
3
%
2
(3)
24.
3%
(4)
1
%
3
Find the % error in K. The period of oscillation of spring pendulum is given by T  2
m
where m is
k
100 gm and is know to have 0.1 gm accuracy. The period is about 2 s. The time of 100 oscillations is
measured by a stop watch of least count 0.1 s.
25.
(1)
0.1%
(2)
1%
(3)
0.2%
(4)
0.8%
find the % error in measuring X. The physical quantity X is related to four variables a, b, c and d as
follows, X 
a 2b 3
. Errors in measurement of a, b, c, d are 1%, 3%, 2% and 2% respectively. What
c d
is percentage error in quantity X?
26.
27.
28.
29.
30.
(1)
12%
(2)
8%
(3)
14%
(4)
5%
Calculate the thickness of cylinder. The inner diameter and outer diameter of a hollow cylinder are
measured to be (5.3 ± 0.1) cm and (6.8 ± 0.1) respectively.
(1)
0.8 ± 0.2
(2)
1.5 ± 0.1
(3)
1.5 ± 0.2
(4)
0.8 ± 0.1
Number of significant figure in 6.020 × 1023 is
(1)
3
(2)
24
(3)
4
(4)
1
Find the dimensional formula for l, if x = k sin(klt), where x is displacement and t is time
(k, l = constant)
(1)
[M0L0T0]
(2)
[M0L1T0]
(3)
[M0L–1T–1]
(4)
[ML–1T–1]
If y represents mass and x represents velocity, then dimensional formula for
(1)
[M0L0T0]
(2)
[ML–3T3]
(3)
[M3L–3T3]
(4)
[M3L3T–3]
d 3y
dx 3
Find the area of rectangle, if length of a rectangle is 2.1 m and width is 1.62 m
(1)
3.402 m2
(2)
3.4 m2
(3)
3.40 m2
(4)
3 m2
will be