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NEET PHYSICSUNITS AND MEASUREMENTSMedium

Question

The density of material in the CGS system of units is 4 g/cm34\text{ g/cm}^3. In a system of units in which unit of length is 10 cm10\text{ cm} and unit of mass is 100 g100\text{ g}, the value of density of material in this system will be:

A

0.40.4

B

4040

C

400400

D

0.040.04

Step-by-Step Solution

The magnitude of a physical quantity remains constant regardless of the system of units used. Thus, n1u1=n2u2n_1 u_1 = n_2 u_2. The dimensional formula for density is [ML−3][M L^{-3}]. We have n1=4n_1 = 4, M1=1 gM_1 = 1\text{ g}, L1=1 cmL_1 = 1\text{ cm}. In the new system, M2=100 gM_2 = 100\text{ g}, L2=10 cmL_2 = 10\text{ cm}. Using the relation n2=n1[M1M2]a[L1L2]bn_2 = n_1 \left[\frac{M_1}{M_2}\right]^a \left[\frac{L_1}{L_2}\right]^b, where a=1a = 1 and b=−3b = -3: n2=4×[1 g100 g]1×[1 cm10 cm]−3n_2 = 4 \times \left[\frac{1\text{ g}}{100\text{ g}}\right]^1 \times \left[\frac{1\text{ cm}}{10\text{ cm}}\right]^{-3} n2=4×(1100)×(10)3=4×1000100=40n_2 = 4 \times \left(\frac{1}{100}\right) \times (10)^3 = 4 \times \frac{1000}{100} = 40. Therefore, the value of density in the new system is 4040.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from UNITS AND MEASUREMENTS. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSUNITS AND MEASUREMENTSdensitymaterialsystemsystemlength

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