JEE Advance - Physics (2016 - Paper 2 Offline - No. 5)
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 (C1) has 10 equal divisions that correspond to 9 main scale
divisions. The Vernier scale of the other caliper (C2) 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 C1 and C2 respectively, are
2.85 and 2.82
2.87 and 2.83
2.87 and 2.86
2.87 and 2.87
Explanation
In both calipers C1 and C2, 1 cm is divided into 10 equal divisions on the main scale. Thus, 1 division on the main scale is equal to xm1 = xm2 = 1 cm/10 = 0.1 cm.
In calipers C1, 10 equal divisions on the Vernier scale are equal to 9 main scale divisions.
Thus, 1 division on the Vernier scale of C1 is equal to xv1 = 9xm1/10 = 0.09 cm.
In calipers C2, 10 equal divisions on the Vernier scale are equal to 11 main scale divisions.
Thus, 1 division on the Vernier scale of C2 is equal to xv2 = 11xm2/10 = 0.11 cm.
Let main scale reading be MSR and vth division of the Vernier scale coincides with mth division of the main scale (m is counted beyond MSR). The value measured by this calipers is
X = MSR + x = MSR + mxm $$-$$ vxv .........(1)
In calipers C1, MSR1 = 2.8 cm, m1 = 7 and v1 = 7 and in calipers C2, MSR2 = 2.8 cm, m2 = 8 and v2 = 7. Substitute these values in equation (1) to get
X1 = MSR1 + m1xm1 $$-$$ v1xv1
= 2.8 + 7(0.1) $$-$$ 7(0.09) = 2.87 cm.
X2 = MSR2 + m2xm2 $$-$$ v2xv2
= 2.8 + 8(0.1) $$-$$ 7(0.11) = 2.83 cm.
In calipers C1, 10 equal divisions on the Vernier scale are equal to 9 main scale divisions.
Thus, 1 division on the Vernier scale of C1 is equal to xv1 = 9xm1/10 = 0.09 cm.
In calipers C2, 10 equal divisions on the Vernier scale are equal to 11 main scale divisions.
Thus, 1 division on the Vernier scale of C2 is equal to xv2 = 11xm2/10 = 0.11 cm.
Let main scale reading be MSR and vth division of the Vernier scale coincides with mth division of the main scale (m is counted beyond MSR). The value measured by this calipers is
X = MSR + x = MSR + mxm $$-$$ vxv .........(1)
In calipers C1, MSR1 = 2.8 cm, m1 = 7 and v1 = 7 and in calipers C2, MSR2 = 2.8 cm, m2 = 8 and v2 = 7. Substitute these values in equation (1) to get
X1 = MSR1 + m1xm1 $$-$$ v1xv1
= 2.8 + 7(0.1) $$-$$ 7(0.09) = 2.87 cm.
X2 = MSR2 + m2xm2 $$-$$ v2xv2
= 2.8 + 8(0.1) $$-$$ 7(0.11) = 2.83 cm.
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