While measuring the diameter of a sphere with a Vernier caliper, the $M . S . R$ and $V . C . D$ were found to be $30$ and $3$ divisions, respectively. What is the radius of the sphere, if the number of Vernier scale divisions is $10$ , and on the main scale, $1 c m$ is divided into $10$ divisions ?

$1.515 c m$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$1.565 c m$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$1.515 m m$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$1.555 c m$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
$1.515 c m$

Step 1: Given formula
$M . S . D$ stands for Main Scale Division.
$M S R$ stands for Main Scale Reading
$V . S . D$ stands for Vernier Scale Division.
$M S R = 30 m m = 3 c m V . C . D = 3$
$N u m b e r o f V . S . D = 10$
Formula of $L e a s t c o u n t = \frac{1 M S D}{N u m b e r o f v e r n i e r d i v i s i o n}$
Step 2: Calculation for radius
Least Count, $L . C = \frac{1 M . S . D}{N u m b e r o f V . S . D}$
$1 M S D = \frac{1 c m}{10} = 0.1 c m$
$L e a s t c o u n t = \frac{1 M S D}{N u m b e r o f v e r n i e r d i v i s i o n} = \frac{0.1 c m}{10} = 0.01 c m$
$D i a m e t e r o f s p h e r e = M . S . R + (V . C . D) \times L . C = 3 c m + 3 \times 0.01 c m = 3.03 c m$
We know Radius is half of the diameter
Hence radius is $r = \frac{d i a m e t e r o f s p h e r e}{2} = \frac{3.03}{2} = 1.515 c m$
Hence correct option is A.

Suggest Corrections

Join BYJU'S Learning Program