# measurement and system of units

```CH 2 JEE
1.The period of a body under is represented by T  P a D b S c ; where P is pressure, D is density and S is surface tension. The value
1 3
1
1
, , 
(d) 1, 2 ,
2 2
2
3
X
2.The dimensions of physical quantity X in the equation Force 
is given by (a) M 1 L4T 2 (b) M 2 L2T 1
density
of a, b and c are
(a) 
3 1
, ,1 (b)-1, -2, 3
2 2
(c) M 2 L2T 2 (d) M 1L2T 1
3.Dimensions of CR are those of
(c)
(a)frequency
(b)energy
(c)time period
(d)current
4.A force F is given by F  at  bt , where t is time. What are the dimensions of a and b
2
(a) MLT 3 and ML2T 4
(b) MLT 3 and MLT 4
(c) MLT 1 and MLT 0
5.The physical quantity which has dimensional formula as that of
(a)force
(b)power
(c)pressure
(d) MLT 4 and MLT 1
energy
is
mass  length
(d)acceleration
6.If L, C and R denote the inductance, capacitance and resistance respectively, the dimensional formula for C 2 LR is
(a)  ML2T 1 I 0 
(c)  M 1 L2T 6 I 2 
(b)  M 0 L0T 3 I 0 
(d)  M 0 L0T 2 I 0 
7.The dimensional formula for young’s modulus is (a) ML1T 2 (b) M 0 LT 2 (c) MLT 2
(d) ML2T 2
8.If force ( F), length (L) and time (T) are assumed to be fundamental units, then the dimensional formula of the mass will be
(a) FL1T 2
(b) FL1T 2
(c) FL1T 1
(d) FL2T 2
9.In a system of units if force (F), acceleration (A) and time (T) are taken as fundamental units then the dimensional formula of
energy is
(a) FA2T
(b) FAT 2
(c) F 2 AT
(d)FAT
10.The period of oscillation of a simple pendulum is given by T= 2
l
where l is about 100 cm and is known to have 1mm
g
accuracy. The period is about 2s. The time of 100 oscillations is measured by a stop watch of least count 0.1 s. The percentage
error in g is
(a)0.1 %
(b)1 %
(c)0.2 %
(d)0.8 %
11.The percentage errors in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum
error in the estimation of the kinetic energy obtained by measuring mass and speed (a)11 % (b)8 % (c)5 %
(d)1 %
12.A body travels uniformly a distance of 13.8  0.2  m in a time  4.0  0.3 s . The velocity of the body within error limits is
(a)  3.45  0.2  ms 1 (b)  3.45  0.3 ms 1 (c)  3.45  0.4  ms 1 (d)  3.45  0.5 ms 1
V
where V  100  5 volts and i  10  0.2 amperes. What is the total error in R
i
5
(b)7%
(c)5.2%
(d) %
2
13.The resistance R 
(a)5%
14.The period of oscillation of a simple pendulum in the experiment is recorded as 2.63 s, 2.56 s, 2.42 s, 2.71 s and 2.80 s
respectively. The average absolute error is (a)0.1 s
(b)0.11 s
(c)0.01 s
(d)1.0 s
15.According to joule’s law of heating, heat produced H  I 2 Rt , where I is current, R is resistance and t is time. If the errors in
the measurement of I, R and t are 3%, 4% and 6% respectively then error in the measurement of H is
(a)  17 %
(b)  16 %
(c)  19 %
(d)  25 %
16.The percentage errors in the measurement of length and time period of a simple pendulum are 1 % and 2 % respectively.
Then the maximum error in the measurement of acceleration due to gravity is (a)8 %
(b)3 % (c)4 %
(d)6 % (e)5 %
1
17. A physical quantity P is given by P 
A3 B 2
4
C D
3
2
. The quantity which brings in the maximum percentage error in P is
(a)A
(b)B
(c)C
(d)D
18. A sphere of radius ‘r’ moving in a viscous medium with velocity ‘v’. If the resistive force on it is given by F  6 rv , then
1 1
dimensional formula of coefficient of viscocity  will be.......... (a) ML T
1
(b) MT
2
(c) MLT
3
(d) ML
19. One planet is observed from two diametrically opposite points A and B on the earth. The angle subtended at the planet by
the two directions of observations is 1.8 . given the diameter of the earth to be about 1.276  107 m. What will be distance of
the planet from the earth ?
(a) 13.8  108 m
(b) 3.84 106 km
(c) 4.06 108 m
(d) 4.06 106 km
20. Force F  A cos Bx  C sin Dt , where x in meter and t in time then find dimensional formula of
0 0 0
(a) M L T
0 0 1
(b) M L T
0 1 0
(c) M LT
0 1 1
(d) M LT
D
.
B
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