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**Single Correct Option:****Ques 1: Percentage error in the measurement of mass and speed are 2% and 3% respectively. The error in the estimate of kinetic energy obtained by measuring mass and speed will be (a) 12% (b) 10% (c) 8% (d) 2%**

âˆ´

âˆ´ Maximum error = 2% + 2 (3%)

In the estimate of, kinetic energy (K) = 8%

Option (c) is correct.

= 4% + 3(3%)

= 13%

Option (d) is correct.

âˆ´ Permissible error in pressure (p)

= 4% + 2 (2%)

= 8%

Option (a) is correct.

â‡’

âˆ´ Percentage increase in pressure = 100/9

= 11.1

Option (a) is correct.

âˆ´ Error in the measurement of kinetic energy (K)

= 2 x 100%

= 200%

Option (d) is correct.

3400 = 3.400 x 10

âˆ´ Number of significant figures = 2

Option (d) is correct.

A = 3.124 m x 3.002 m

= 9.378/248 m

= 9.378 m

Option (a) is correct.

âˆ´ Decrease in R (radius) by 2% world increase g by 4% and decrease K (rotational kinetic energy) by 4%.

Option (b) is correct.**Ques 9: The heat generated in a circuit is dependent upon the resistance, current and time for which the current is flown. If the error in measuring the above are 1%, 2% and 1% respectively. The maximum error in measuring the heat is ****(a) 8% ****(b) 6% ****(c) 18% ****(d) 12%****Ans: **6%**Solution:**

Heat (H) = I^{2} Rt

âˆ´ Maximum error in measuring heat (H)

=2 (2%) + 1% + 1%

= 6%

Option (b) is correct.**Ques 10: ****The length, breadth and thickness of a block are given by / = 12 cm, b = 6 cm and t =2.45 cm. The volume of the block according to the idea of significant figures should be (a) 1 x 10 ^{2} cm^{3} (b) 2 x 10^{2} cm^{3} (c) 1.763 x 10^{2} cm^{3} (d) None of these**

V = lbt

Option (b) is correct.

i.e., Ir

i.e., if 'r' is increased by 2%,

the intensity will decrease by 4%.

Option (d) is correct.

Option (b) is correct.

= 3(1%)

= 3%

Option (c) is correct.

a

âˆ´ a = 6

â‡’ V = 6

Option (b) is correct.

Option (a) is correct.

**Solution: **

(given)

We know that

Q = It

â‡’

Option (a) is correct.**Ques 17: A physical quantity A is dependent on other four physical quantities p, q, r and s as given by ****The percentage error of measurement in p , q , r and s are 1%, 3%, 0.5% and 0.33% respectively, then the maximum percentage error in A is****(a) 2% (b) 0% (c) 4% (d) 3%**

Option (c) is correct.

= 2mm/4 = 0.5 mm

= 0.1 mm Zero error = - 30 x 0.01 mm = -0.3 mm

(â€“ive sign, zero of circular scale is lying above observed reading of plate thick)

= 2 MSR + 20 CSR

= (2 Ã— 0.5 mm) + (20 Ã— 0.01 mm) = 1 mm + 0.2 mm = 1.2 mm.

Plate thickness (corrected reading)

= observed reading - zero error = 1.2 mm + 0.3 mm = 1.5 mm

Option (d) is correct.

More than One Correct Options:

Maximum percentage error in x:

= 1 (% error in a) + 2 (% error in b) +3 (% error in c)

= 15%

Reason: The least count of screw gauge is directly proportional to the number of divisions on circular scale.

Least count of screw gauge

Less the value of pitch, less will be least count of screw gauge leading to len uncertainty that is more accuracy in the measurement.

Thus, assertion is true.

From the above relation we conclude that least count of screw gauge is inversely proportional to the number of divisions of circular scale.

Thus reason is false.

Option (c) is correct.

Column-I | Column-II |

(a) GM_{e}M_{s} | (p) [M^{2}L^{2}T^{-3}] |

(q ) [ML^{3}T-2] | |

(r) [L^{2}T^{-2}] | |

(s) None |

**Ans:** (a) â†’ q (b) â†’ r (c) â†’ r (d) â†’ r**Solution:****(d) **

â‡’

= [L^{2} T^{â€“2}]

âˆ´ (d) â†’ (r)