Hooke S Law

1. Define Variables:
   • Let be the number of sums Asim got right.
   • Let be the number of sums Asim got wrong.
2. Formulate Equations Based on the Problem Statement:
   • "Asim got thrice as many sums wrong as he got right": This translates to the equation:

• "If he attempted 60 sums in all": This means the total number of sums (right + wrong) is 60.

1. Solve the System of Equations:
   • Substitute the expression for from Equation (1) into Equation (2):

• Let be the number of sums Asim solved incorrectly (got wrong).

1. Formulate Equations based on the Given Information:
   • "Asim got thrice as many sums wrong as he got right": This means the number of wrong sums is 3 times the number of right sums.

• "If he attempted 60 sums in all": The total number of sums attempted is the sum of those solved correctly and those solved incorrectly.

1. Solve the System of Equations:
   • We can substitute the expression for from equation (1) into equation (2):

• Combine the terms with :

• Solve for by dividing both sides by 4:

1. Answer the Question:
   • The question asks for the number of sums Asim solved correctly, which is .
   • We found .
   • (Optional check: If , then . Total sums = . This matches the problem statement.)
2. Compare with Options: The calculated value is 15.

The correct option is (e) 15.

Given: Three identical masses form an isosceles right triangle with sides along the positive and axes. The springs have rest length , and the two equal triangle sides are of length .

Let the positions of the three masses be:

• At origin:
• On x-axis:
• On y-axis:

We analyze the force on the mass at :

- It is connected to the mass at the origin with a spring stretched by (since rest length is ). - Force from this spring is along the negative x-axis: $ (0, 2l_0) 2\sqrt{2}l_0 - l_0 = (2\sqrt{2} - 1)l_0 (2l_0, 0) (0, 2l_0) k = 1 l_0 = 1 \frac{1}{\sqrt{2}} \approx 0.707 2 - 0.707 \approx 1.293 $
Answer: (e) a = -2 and b = 1