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

In an experiment four quantities a , b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as $P=\frac{a^3{b}^2}{cd}$. % error in P is

(1) 14%

(2) 10%

(3) 7%

(4) 4%

A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level.  If screw gauge has a zero error of -0.004 cm, the correct diameter of the ball is 

(1) 0.053 cm

(2) 0.525 cm

(3) 0.521 cm

(4) 0.529 cm

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) $L, LT and T^2$

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) $\left[M^{-1}{L}^3{T}^{-2}\right]$

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

Find the zero correction in the given figure. 

1. \(0.4\) mm

2. \(0.5\) mm

3. \(-0.5\) mm

4. \(-0.4\) mm

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