$$5.74$$ g of a substance occupies $$1.2~\text{cm}^3$$. Its density by keeping the significant figures in view is:
1. $$4.7333~\text{g/cm}^3$$
2. $$3.8~\text{g/cm}^3$$
3. $$4.8~\text{g/cm}^3$$
4. $$3.7833~\text{g/cm}^3$$

Subtopic:  Dimensions |
83%
From NCERT
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

The SI unit of energy is $$\mathrm{J = \text{kg}\left(m\right)^{2} s^{- 2}}$$; that of speed $$v$$ is $$\text{ms}^{- 1}$$ and of acceleration $$a$$ is $$\text{ms}^{- 2}$$. Which of the formula for kinetic energy ($$K$$) given below can you rule out on the basis of dimensional arguments (m stands for the mass of the body)?

 (a) $$K={m^{2} v^{3}}$$ (b) $$K=\dfrac{1}{2}mv^{2}$$ (c) $$K= ma$$ (d) $$K =\dfrac{3}{16}mv^{2}$$ (e) $$K = \dfrac{1}{2}mv^2+ ma$$

Choose the correct option:

 1 (a), (c) & (d) 2 (b) & (d) 3 (a), (c), (d) & (e) 4 (a), (c) & (e)

Subtopic:  Dimensions |
From NCERT
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

Let us consider an equation $$\dfrac{1}{2}mv^2=mgh$$ where $$m$$ is the mass of the body, $$v$$ its velocity, $$g$$ is the acceleration due to gravity and $$h$$ is the height. The equation is:

 1 dimensionally correct. 2 dimensionally incorrect. 3 can not be checked by dimensional analysis. 4 can't say anything.

Subtopic:  Dimensions |
80%
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length $$(l)$$, the mass of the bob $$(m)$$ and acceleration due to gravity $$(g)$$. Expression for its time period is:

1.  $$T = \dfrac{1}{2 \pi} \sqrt{\dfrac{l}{g}}$$

2.  $$T = 2 \pi \left(\dfrac{l}{g}\right)$$

3.  $$T = 2 \pi \sqrt{\dfrac{l}{g}}$$

4.  $$T = 2 \pi \sqrt{\dfrac{g}{l}}$$

Subtopic:  Dimensions |
77%
From NCERT
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints