2N division on main scale of a vernier calliper coincide with 15(μ -1)λ division of the vernier scale if each division on main scale is of b units, least count of instrument is

Question

2N division on main scale of a vernier calliper coincide with 15(μ -1)λ division of the vernier scale if each division on main scale is of b units, least count of instrument is (A)  25(μ -1)λ  (B)  (25λ /(μ -1))  (C)  vP=0, vQ=v  (D)  vP=v, vQ=0

Tardigrade Admin · Accepted Answer

According to the question (2N+1)VSD=2N MSD ∴ 1VSD=(2N/2N+1)MSD Least count = (1MSD - 1VSD) (value of MSD) ; 1VSD=(2N/2N+1)MSD =( (2N+1-2N/2N+1) )b=(1/(2N+1))

Q. 2N division on main scale of a vernier calliper coincide with $15 (μ - 1) λ$ division of the vernier scale if each division on main scale is of b units, least count of instrument is

$25 (μ - 1) λ$

$\frac{25 λ}{( μ - 1 )}$

$v_{P} = 0, v_{Q} = v$

$v_{P} = v, v_{Q} = 0$

According to the question $(2 N + 1) V S D = 2 N MS D$ $∴$ $1 V S D = \frac{2 N}{2 N + 1} MS D$ Least count = (1MSD - 1VSD) (value of MSD) ; $1 V S D = \frac{2 N}{2 N + 1} MS D$ $= (\frac{2 N + 1 - 2 N}{2 N + 1}) b = \frac{1}{( 2 N + 1 )}$

Q. 2N division on main scale of a vernier calliper coincide with 15(μ−1)λ division of the vernier scale if each division on main scale is of b units, least count of instrument is

25(μ−1)λ

(μ−1)25λ​

vP​=0,vQ​=v

vP​=v,vQ​=0