Question 269: Units , Dimensions and Error Analysis

Question

There are two Vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale.
The Vernier scale of one of the calipers (C
1
) has 10 equal divisions that correspond to 9 main scale
divisions. The Vernier scale of the other caliper (C
2
) has 10 equal divisions that correspond to 11 main
scale divisions. The readings of the two calipers are shown in the figure. The measured values (in cm) by
calipers C
1
and C
2
respectively, are

Accepted Answer

In both calipers C
1
and C
2
, 1 cm is divided into 10 equal divisions on the main scale. Thus, 1 division on the main scale is equal to x
m1
= x
m2
= 1 cm/10 = 0.1 cm.
In calipers C
1
, 10 equal divisions on the Vernier scale are equal to 9 main scale divisions.
Thus, 1 division on the Vernier scale of C
1
is equal to x
v1
= 9x
m1
/10 = 0.09 cm.
In calipers C
2
, 10 equal divisions on the Vernier scale are equal to 11 main scale divisions.
Thus, 1 division on the Vernier scale of C
2
is equal to x
v2
= 11x
m2
/10 = 0.11 cm.
Let main scale reading be MSR and v
th
division of the Vernier scale coincides with m
th
division of the main scale (m is counted beyond MSR). The value measured by this calipers is
X = MSR + x = MSR + mx
m
$$-$$ vx
v
.........(1)
In calipers C
1
, MSR
1
= 2.8 cm, m
1
= 7 and v
1
= 7 and in calipers C
2
, MSR
2
= 2.8 cm, m
2
= 8 and v
2
= 7. Substitute these values in equation (1) to get
X
1
= MSR
1
+ m
1
x
m1
$$-$$ v
1
x
v1
= 2.8 + 7(0.1) $$-$$ 7(0.09) = 2.87 cm.
X
2
= MSR
2
+ m
2
x
m2
$$-$$ v
2
x
v2
= 2.8 + 8(0.1) $$-$$ 7(0.11) = 2.83 cm.

Answer

2.85 and 2.82

Answer

2.87 and 2.83

Answer

2.87 and 2.86

Answer

2.87 and 2.87

Units , Dimensions and Error Analysis

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