Dimensional Analysis Numerical Based on Conversion of Units of One System into the Units of Other System of Class 11 ISC Nootan Physics Solutions Ch-3. Step by step solutions of Kumar and Mittal Physics of Nageen Prakashan as council latest prescribe guideline for upcoming exam. Visit official Website CISCE for detail information about ISC Board Class-11 Physics.

## Dimensional Analysis Numerical Based on Conversion of Units of One System into Units of Other System

Ch-3 Class 11 ISC Nootan Physics Solutions Kumar and Mittal Physics of Nageen Prakashan

Board | ISC |

Class | 11 |

Subject | Physics |

Writer | Kumar and Mittal |

Publication | Nageen Prakashan |

Chapter-3 | Dimensional Analysis |

Topics | Numericals Based on Conversion of Units of One System into the Units of Other System |

Academic Session | 2024-2025 |

### Numerical Based on Conversion of Units of One System into the Units of Other System

Ch-3 Dimensional Analysis Class 11 ISC Nootan Physics Solutions Kumar and Mittal Physics of Nageen Prakashan

**Question-17: The velocity of a body is 36 km /h. Express it in SI units.**

**Answer- **Here, we have to convert velocity from km/h to m/s

we know that, 1km = 1000m and 1 h = 60 * 60 = 3600s

=>36km/h = 36 * 1000 / 60 * 60 = 360 / 36 = 10 m/s.

**Question-18: The velocity of sound in air is 332 m/s. Convert it in km/h km /h**

**Answer- **We know that 1m = 10 ^-3 km

also, is = 1/3600 h

velocity = 332m/s => 332 *[10^-3km / (1/3600)h]

=>1195 km/h.

**Question-19: A body has an acceleration of 5 km/h^2 . Find its value in CGS system.**

**Answer- **we know that, 1km =1000m = 100000 cm

and 1 h = 3600s

thus, 5km/h^2 = 5 * 100000 / 3600^2

= **0.0386 cm/s^2.**

**Question-20: The value of a force is 36 units in a system having metre, kilogram and minute as fundamental units. What will be its value in CGS system?**

**Answer- **Given that force is – F = 36 k g . m/min²

We know, 1 kg = 1000 g

1 m = 100 cm and

1 min = 60 s

Substitute this values –

F = 36 × 1000 × 100 / 60²

⇒ F = 1000 g.cm/s²

**⇒ F = 1000 dyne**

**Question-21: The unit of work is joule (J) in the SI system and erg in the CGS system. Find number of ergs in 1 joule.**

**Answer- **Dimensionally,

[Energy]=[mass]×[velocity]^2

= mass×(length/time)^2=ML^2T^−2

Thus, 1joule=(1kg)(1m)^2(1s)^−2

and 1 erg=(1g)(1cm)^2(1s)^−2

1 joule1erg=(1kg1g)(1m1cm)^2(1s1s)^−2

= (1000g1g)(100cm1cm)^2=1000×10000=**10^7.**

**Question-22: Express 1 MW (megawatt) power in ergs a system whose fundamental units are 10 kg, 1 dm (decimeter) and 1 minute.**

**Answer- **One megawatt power can be expressed as –

1 MW = 10^6 W

But we know, 1 W = m^2·kg/s^3

1 MW = 10^6 m^2·kg·s^-3

Also, 1 m = 10 dm, 1 s = 1/60 min, 1 kg = 10/10 kg

⇒ 1 MW = 10^6 × (1 m)^2 × (1 kg) / (1 s)^3

⇒ 1 MW = 10^6 × (10 dm)^2 × (10/10 kg) / (1/60 min)^3

**1 MW = 2.16×10^12 dm^2.10kg/min^3**

**Question-23: Express 1 atmospheric pressure (10^5 N m^-2)in CGS system.**

**Answer- **1 atm = 10⁵ N/m².

Now, the CGS unit of pressure is dyne/cm², which is also called Barye, and denoted by Ba.

Further, 1 N/m² = 10 dyne/cm².

Here, the pressure given is 10⁵ N/m². Thus, in the CGS system,

⇒ 10⁵ N/m² = 10⁵ × 10 dyne/cm²

=> 10⁵ N/m² = **10⁶ dyne/cm²**

—: end of Dimensional Analysis Numerical Based on Conversion of Units into Other System for Class 11 ISC Nootan Physics Kumar and Mittal Physics :—

Return to : **– Nootan Solutions for ISC Physics Class-11 Nageen Prakashan**

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