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When units of mass, length, and time are taken as \(10~\text{kg}, 60~\text{m}~\text{and}~60~\text{s}\) respectively, the new unit of energy becomes \(x\) times the initial SI unit of energy. The value of \(x\) will be:

1. \(10\)

2. \(20\)

3. \(60\)

4. \(120\)

Subtopic: Â Dimensions |

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Which of the following relations is dimensionally wrong? [The symbols have their usual meanings]

1. \(s= ut+\frac{1}{6}at^2\)

2. \(v^2= u^2+\frac{2as^2}{\pi}\)

3. \(v= u-2at\)

4. All of these

Subtopic: Â Dimensions |

Â 67%

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In which of the following, the number of significant figures is different from that in the others?

1. \(2.303~\text{kg}\)

2. \(12.23~\text{m}\)

3. \(0.002\times10^{5}~\text{m}\)

4. \(2.001\times10^{-3}~\text{kg}\)

Subtopic: Â Significant Figures |

Â 88%

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If \(\int \frac{d x}{\sqrt{a^2-x^2}}=a^n \sin ^{-1} \frac{x}{a}\) is dimensionally correct, then the value of \(n\) will be:

1. \(1\)

2. \(\text{zero}\)

3. \(\text-1\)

4. \(2\)

Subtopic: Â Dimensions |

Â 63%

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In an experiment, the height of an object measured by a vernier callipers having least count of \(0.01~\text{cm}\) is found to be \(5.72~\text{cm}\). When no object is there between jaws of this vernier callipers, the reading of the main scale is \(0.1\) cm and the reading of the vernier scale is \(0.3~\text{mm}\). The correct height of the object is:

1. \( 5.72 ~\text{cm} \)

2. \( 5.59~\text{cm} \)

3. \( 5.85~\text{cm} \)

4. \( 5.69~\text{cm} \)

Subtopic: Â Measurement & Measuring Devices |

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A thin wire has a length of \(21.7~\text{cm}\) and a radius of \(0.46~\text{mm}\). The volume of the wire to correct significant figures is:

1. | \( 0.15~ \text{cm}^3 \) | 2. | \( 0.1443~ \text{cm}^3 \) |

3. | \( 0.14~ \text{cm}^3 \) | 4. | \( 0.144 ~\text{cm}^3\) |

Subtopic: Â Significant Figures |

Â 64%

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If \({x}=\frac{{a} \sin \theta+{b} \cos \theta}{{a}+{b}},\) then:$$

1. | the dimensions of \(x\) and \(a\) must be the same |

2. | the dimensions of \(a\) and \(b\) are not the same |

3. | \(x\) is dimensionless |

4. | none of the above |

Subtopic: Â Dimensions |

Â 64%

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Two resistors \(R_1 = (3.0\pm0.3)~\Omega\) and \(R_2 = (5.0 \pm0.1)~\Omega\) are connected in parallel. The equivalent resistance, \(R_{eq}\), will be:

**Hint:** \({1 \over R_{eq}} = {1 \over R_{1}} + {1 \over R_{2}} \)

1. \(1.9\pm0.07~\Omega\)

2. \(1.9\pm0.1~\Omega\)

3. \(2.9\pm0.2~\Omega\)

4. \(2.9\pm0.3~\Omega\)

Subtopic: Â Errors |

Â 51%

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Find the thickness of the wire. The least count is \(0.01\) mm. The main scale reads: (in mm)

1. \(7.62\)

2. \(7.63\)

3. \(7.64\)

4. \(7.65\)

Subtopic: Â Measurement & Measuring Devices |

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The pitch of a screw gauge is \(1~\)mm and there are \(100\) divisions on the circular scale. While measuring the diameter of a wire, the linear scale reads \(1\) mm and \(47\)^{th} division on the circular scale coincides with the reference line. The length of the wire is \(5.6\) cm. Curved surface area (in cm^{2}) of the wire in appropriate number of significant figures will be:

1. \(2.4\) cm^{2}

2. \(2.56\) cm^{2}

3. \(2.6\) cm^{2}

4. \(2.8\) cm^{2}

Subtopic: Â Measurement & Measuring Devices |

Â 55%

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