India · Class 11 · Practice Sheet 15

1. 1.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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2. 2.

   Find the gravitational potential energy of a 48 kg object raised 35 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   ₹3,500 is invested at 6% compound interest per annum for 5 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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4. 4.

   Find the force needed to accelerate a 42 kg mass at 2.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A cylinder has radius 8 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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6. 6.

   A right-angled triangle has legs of 17 cm and 8 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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7. 7.

   Solve using the quadratic formula: x² + 3x + 2 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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8. 8.

   Find the gravitational potential energy of a 29 kg object raised 39 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A force of 59 N moves an object 34 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    Find the force needed to accelerate a 45 kg mass at 1.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    Find the population standard deviation of: 11, 5, 10, 9, 12 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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12. 12.

    A device runs at 193 V drawing 6.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A force of 403 N acts on an area of 2.9 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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14. 14.

    A current of 3.8 A flows through a 11 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    Two masses 4,500 kg and 660 kg are 2 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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16. 16.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 1 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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17. 17.

    A force of 59 N moves an object 2 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A wave has frequency 44 Hz and wavelength 4.6 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Find the sum of the first 4 terms of a geometric series with first term a = 6 and common ratio r = 2.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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20. 20.

    A cone has base radius 9 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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