1
Yakeen 2.0 (2024)
Unit and Dimensions
1.
2.
3.
Which of the following is not a dimensionless
physical quantity
(1) dielectric constant
(2) specific gravity
(3) coefficient of performance
(4) relative acceleration
7.
Find value of one pascal in C.Gs unit (g cm–1 s–2)
(1) 10
(2) 100
(3) 1/10
(4) 1000
8.
If force acting on the object F = t sin (x) e−rt then
find dimension of ,  and .
(1) [MLT–3 L T2]
(2) [MLT–2 L–1 T–2]
(3) [MLT–3 L–1 T–2]
(4) [MLT–1 L–1 T–2]
Which of the following combination of physical
quantity can be considered as a fundamental physical
quantity
(1) Work, energy, torque
(2) Torque, force, mass
(3) Torque, radius, force
(4) Impulse, momentum, time
9.
If n is measured numerical value and u is a unit then
which of the following is correct relation :
10.
n
= cos t n
u
(3) nu = cos tn
(1)
(2)
u
= cos t n
n
11.
4.
5.
6.
Which of the following relation is wrong.
(1) 1 Ampere × 1 ohm = 1 volt
(2) 1 newton per coulomb = 1 volt per meter
(3) 1 watt × 1 sec = 1 joule
(4) 1 killowatt-hr = 1 J
If universal gravitational constant G, speed of light c
and mass taken as fundamental P.Q. then dimension
of area = G M C then value of ,  and  are –
(1) –2, –2, 4
(2) 3, 3, –2
(3) 2, 2, – 4
(4) –3, –3, 2
In new system of unity, unit of mass is  kg, unit of
length  m and unit of time  sec then unit of energy
will be
(1)  2 –2
(2) –1  –2 2
(3) 2  –2
(4)  2 –1
Assignment 01
2
 x 
Velocity of object V =  exp  −  , find
 t 
dimension of .
(1) [L2 T2]
(2) [L–2 T–2]
(3) [L2 T–2]
(4) [L–2 T2]
Vander Wall’s gas equation for a n number of moles
a 

is given by the formula  P + 2  = nRT then
V 

dimension of R will be :t

Given that power P = A sin  − x  then which of


the following is correct
(1) Dimension of t same as 
(2) Dimension of  same as x
(3) Dimension of  same as inverse of x
(4) Both (1) and (3)
12.
Two students A and B carried out an experiment to
measure the time period of a pendulum which in
actual is 5.40 s. Their experimental readings are as
follows :
Students A
5.43 s
5.37 s
5.41 s
5.52 s
Students B
5.32 s
5.34 s
5.30 s
5.29 s
5.51 s
5.33 s
2
13.
18.
If e is charge h Planks constant C = speed of light then
19.
If momentum (P), area (A) and time (t) are taken as
fundamental quantity, then dimension of energy will
be
(1) [P–1 A–1 t–1]
(2) [P–1 A1/2 t–1]
(3) [P2 A1 t1]
(4) [P1 A1/2 t]
20.
Equation
21.
If energy of object given by E =
2
dimension of
e
.
40 hc
(1) [M]
(3) [ML]
14.
(2) [L]
(4) [M0 L0 T0]
Find dimension of given expression :
Magnetic moment
(i)
Angular momentum
(ii)
hCS
G
L
R
1
(vi)
RC
(iv)
15.
16.
(iii)
F
qvB
(v)
(00 )−1 2
The relation between time ‘t’ and distance x is given
as t = ax2 + bx where a and b are constant then find
acceleration :
[IIT Adv.-2016]
3
3
(1) 2bv
(2) –2av
2
(3) 2abv
(4) 2av2
Energy of photon and electron is same E then find
ratio of their de-Broglie wavelength where m is mass
of electron, c = speed of light.
(1) c 2mE
12
 2m 
(3) c 

 E 
P−Q
R
(3) PQ – R
PQ
R
(4)
P − R2
Q
(4) 5  2 –2
d2x
dx
+ A + Bx = C then find dimension
2
dt
dt
of A, B and C where x is position and t is time.
(1) [T T2 LT–2]
(2) [T–1 T–2 LT–2]
(3) [T–2 T–1 LT2]
(4) [T T2 LT–2]
A−x
then
Bt
23.
Which of the following dimension same as velocity
E
B
(3) µC
(1)
 2E 
(4) 

 mc 
(2)
(3) 5 –1 2 2
Which of the following has same dimension.
(1) Heat, Temperature
(2) Heat, Power
(3) Specific heat, heat
(4) Heat, Torque
24.
(1)
(2) 5 –1 –2 2
22.
 2Ec 
(2) 

 m 
If P, Q, R having different dimensions, then which of
the following combination can never be a meaningful
quantity.
(1) 5  2 2
dimension of A and B are :
(1) [L MLT–2]
(2) [L M–1 L–1 T]
(3) [MLT–2 L]
(4) [L MLT]
12
17.
In new system of unit if unit of mass  kg, length 
m and unit of time  sec. What will be value of 5 J in
this new system
Then :
(1) Student A is more precise but less accurate
(2) Student B is more precise but less accurate
(3) Student A is more precise as well as accurate
(4) Student B is more precise as well as accurate
(2) (µ0 0)–1/2
(4) All of these
If y is energy and x is length then dimension of
same as :
(1) Force
(3) Work
(2) Energy
(4) None of these
dy
dx
3
25.
26.
 B
Work done on the object W = A log 1 − 2  then
 t 
dimension of B is
(1) [T2]
(2) [T–2]
(3) [ML2 T–2]
(4) [T]
Sum of dimension of mass, length and time in the
dimensional formula of power will be
(1) Zero
(2) 6
(3) 5
(4) 3
27.
Number of significant zero in 24010 and 4.00 are
respectively
(1) 4, 3
(2) 1, 2
(3) 5, 3
(4) 4, 2
28.
Dimension of angular velocity same as
(1) Angle
(2) R/L
(3) Frequency
(4) both (2) and (3)
29.
Which of the following is not unit less
(1) Velocity gradient
(2) Displacement gradient
Position
Distance
(4) relative permittivity
(3)
30.
A dimensionless quantity
(1) May have unit
(2) Never have unit
(3) Must have unit
(4) Must be unitless
31.
Write answer in correct significant digit 7 × 6 will be
(1) 42
(2) 40
(3) 50
(4) 45
4
Answer Key
1.
(4)
15.
(2)
2.
(2)
16.
(2)
3.
(3)
17.
(1)
4.
(4)
18.
(2)
5.
(3)
19.
(3)
6.
(3)
20.
(2)
7.
(1)
21.
(2)
8.
(2)
22.
(2)
9.
(3)
23.
(1,2)
10.
[ML2 T–2 mol–1 K–1]
24.
(1)
11.
(4)
25.
(1)
12.
(2)
26.
(1)
13.
(4)
27.
(3)
14.
(i)
[A–1 M–1 T]
28.
(4)
(ii)
–2
29.
(1)
(iii) [LT–1]
30.
(1)
(iv) [ML2 T–2]
31.
(2)
(v)
[MT A]
[T]
(vi) [T–1]
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