Question 1 of 17intermediate🔧 ApplyNumerical3 marks

Two objects A and B of mass m and 4m have the same kinetic energy. What is the ratio of the magnitude of velocities of A and B?

Correct Answer

2:1

Exercise: Pause and Ponder | Q: 4 | (Page 8)
For More Understanding

Explanation

The question asks for the ratio of velocities of two objects with different masses but the same kinetic energy. Using the formula for kinetic energy from the textbook, K = 1/2 mv2mv^{2}, we can set up an equation equating the kinetic energies of both objects. By substituting the given masses (m for A and 4m for B) and solving for the ratio of their velocities, we find that object A must move twice as fast as object B to have the same kinetic energy due to its smaller mass.

Solution Steps

  1. Step 1: Write the formula for kinetic energy: K = 1/2 mv²

  2. Step 2: Equate the kinetic energies of object A and object B: 1/2 m(v_A)² = 1/2 (4m)(v_B)²

  3. Step 3: Simplify the equation by cancelling 1/2 and m from both sides: (v_A)² = 4(v_B)²

  4. Step 4: Take the square root of both sides to find the ratio of velocities: v_A / v_B = 4\sqrt{4} = 2

  5. Step 5: Express the ratio as v_A : v_B = 2:1

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