One cm on the main scale of vernier callipers is divided into ten equal parts. If 20 divisions of vernier scale coincide with 8 small divisions of the main scale. What will be the least count of callipers?

1.  0.06 cm

2.  0.6 cm

3.  0.5 cm

4.  0.7 cm

Find the zero correction in the given figure. 

1. \(0.4\) mm

2. \(0.5\) mm

3. \(-0.5\) mm

4. \(-0.4\) mm

The circular division of shown screw gauge are 50. It moves 0.5 mm on main scale in one rotation. The diameter of the ball is 

(1)  2.25 mm

(2)  2.20 mm

(3)  1.20 mm

(4)  1.25 mm

Two full turns of the circular scale of gauge cover a distance of \(1\) mm on scale. The total number of divisions on the circular scale is \(50.\) Further, it is found that screw gauge has a zero error of \(-0.03\) mm. While measuring the diameter of a thin wire a student notes the main scale reading of \(3\) mm and the number of circular scale division in line, with the main scale as \(35.\) The diameter of the wire is:
1. \(3.32\) mm
2. \(3.73\) mm
3. \(3.67\) mm
4. \(3.38\) mm

A pair of physical quantities having same dimensional formula is 

(1) Force and torque

(2) work and energy

(3) force and impulse

(4) linear momentum and angular momentum

The dimensions of universal gravitational constant are

(1) $\left[M{L}^2{T}^{-1}\right]$

(2) $\left[M^{-2}{L}^3{T}^{-2}\right]$

(3) $\left[M^{-2}{L}^2{T}^{-1}\right]$

(4) $\left[M^{-1}{L}^3{T}^{-2}\right]$

The velocity $\nu$ of a particle at time t is given by $\nu =at+\frac{b}{t+c}$, where a, b, and c are constants. The dimensions of a, b and c are respectively.

(1) $L{T}^{-2}, L and T$

(2) $L^2, T and L{T}^2$

(3) $L{T}^2, LT and L$

(4) $L, LT and T^2$

If the dimensions of a physical quantity are given by $\left[M^a{L}^b{T}^c\right]$, then the physical quantity will be

(1) velocity if a = 1, b = 0, c = -1

(2) acceleration if a = 1, b = 1, c = -2

(3) force if a = 0, b = -1, c = -2

(4) Pressure if a = 1, b =-1, c = -2

A student measures the distance traversed in the free fall of a body, initially at rest in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are $e_1 and e_2$, respectively, the percentage error in the estimation of g is

(1) $e_1+2e_2$

(2) $e_1+e_2$

(3) $e_1-2e_2$

(4) $e_2-e_1$

The density of a material in the CGS system of units is 4 g $c{m}^{-3}$. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of density of material will be

(1) 0.04

(2) 0.4

(3) 40

(4) 400