# CBSE Class 11-Physics: Units and Measurement: Test-2: Questions (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 1**:

Show that expression is dimensionally correct, where *v* and *v* represents velocities and is acceleration and represents time.

**Question 2**:

Each of the following equations was given by a student during an examination.

Do the dimensional analysis of each equation and explain why the equations cannot be correct.

**Question 3**:

Suppose that the displacement of an object is related to time according to the expression . What are the dimensions of?

**Question 4**:

Find the unit of pressure.

**Question 5**:

(a) Is it possible for two quantities to have the same dimensions but different units.

(b) Is it possible for two quantities to have same units but different dimensions?

**Question 6**:

Suppose we are told that the acceleration *‘* of a particle moving with uniform speed *’* in a circle of radius is proportional to some power of , say , and some power of . How can we determine the value of and .

**Question 7**:

The mass of a solid cube is , and each edge has a length of . Determine the density of the cube in basic units.

**Question 8**:

The period of a simple pendulum is measured in time units and is described by

Where is the length of the pendulum and is the free fall acceleration in units of length divided by square of time? Show that this equation is dimensionally correct.

**Question 9**:

Estimate the average mass density of a sodium atom assuming its size to be about . (Use the known values of Avogadro՚s number and the atomic mass of sodium) . Compare it with the density of sodium in its crystalline phase: . Are the two densities of the same order of magnitude? If so, why?

**Question 10**:

In the following is in meters, in seconds, in and is in . Find the unit of each combination.

(a)

(b)

(c)