A screw gauge has the least count of \(0.01~\text{mm}\) and there are \(50\) divisions in its circular scale. The pitch of the screw gauge is:
1. \(0.25~\text{mm}\)
2. \(0.5~\text{mm}\)
3. \(1.0~\text{mm}\)
4. \(0.01~\text{mm}\)

Time intervals measured by a clock give the following readings: 
\(1.25\) s, \(1.24\) s, \(1.27\) s, \(1.21\) s and \(1.28\) s. 
What is the percentage relative error of the observations? 
1. \(2\)%
2. \(4\)%
3. \(16\)%
4. \(1.6\)%

The main scale of a vernier calliper has \(n\) divisions/cm. \(n\) divisions of the vernier scale coincide with \((n-1)\) divisions of the main scale. The least count of the vernier calliper is:
1. \(\dfrac{1}{(n+1)(n-1)}\) cm
2. \(\dfrac{1}{n}\) cm
3. \(\dfrac{1}{n^{2}}\) cm
4. \(\dfrac{1}{(n)(n+1)}\) cm

The density of a material in a CGS system of units is \(4~\text{grams/cm}^3\). In a system of units in which the unit of length is \(10~\text{cm}\) and the unit of mass is \(100~\text{grams}\), the value of the density of the material will be:
1. \( 0.04 \)
2. \( 0.4 \)
3. \( 40 \)
4. \(400\)

A student measures the distance traversed in 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 the 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 ratio of the dimension of Planck's constant and that of the moment of inertia is the dimension of:

1. Velocity

2. Angular momentum

3. Time

4. Frequency

Which, of the following pair does not have equal dimensions?

1. Energy and torque

2. Force and impulse

3. Angular momentum and Planck's constant

4. Modulus of Elasticity and pressure

If the error in measurement of the radius of a sphere is 0.1%, then the error in its volume will be:
1. 0.3%
2. 0.4%
3. 0.5%
4. 0.6%