India · Class 11 · Practice Sheet 41

1. 1.

   A cone has base radius 10 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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2. 2.

   A body starts at 5 m/s and accelerates at 3.6 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   Two masses 1,800 kg and 760 kg are 20 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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4. 4.

   Find the sum of the first 6 terms of a geometric series with first term a = 6 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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5. 5.

   Find the force needed to accelerate a 25 kg mass at 5.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A right-angled triangle has legs of 3 cm and 14 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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7. 7.

   A triangle has sides a = 9 cm and b = 9 cm with an included angle C = 90°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

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8. 8.

   A force of 102 N moves an object 3 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A device runs at 106 V drawing 5.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    A current of 2.3 A flows through a 28 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    A cylinder has radius 3 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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12. 12.

    A wave has frequency 655 Hz and wavelength 4.38 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A device runs at 191 V drawing 4.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    Find the momentum of a 53 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    An object has mass 133.2 g and volume 37 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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16. 16.

    In a triangle, a = 15, b = 15 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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17. 17.

    A body starts at 13 m/s and accelerates at 1.3 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    Find the sum of the first 5 terms of a geometric series with first term a = 4 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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19. 19.

    An object with initial velocity 6 m/s accelerates at 4.2 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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20. 20.

    A device runs at 33 V drawing 2.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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