When a rubber band is strecthed by a distance x, it exerts a restoring force of magnitude F = ax +bx², where a and b are constants. The work done in stretching are unstretched rubber-band by L is

• aL² +bL²

• 
• 
• 

This question has statement 1 and statement 2. Of the four choices given after the statements, choose the one that best describes the two statements.
If two springs S₁ and S₂ of force constants k₁ and k₂, respectively, are stretched by the same force, it is found that more work is done on spring S₁ than on spring S₂.

Statement 1: If stretched by the same amount, work done on S1, will be more than that on S₂
Statement 2 : k₁ < k₂

• Statement 1 is false, Statement 2 is true

• Statement 1 is true, Statement 2 is false

• Statement 1 is true, Statement 2 is the correct explanation for statement 1

• Statement 1 is true, Statement 2 is the correct explanation for statement 1

An athlete in the Olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

• 200 J − 500 J

• 2 × 105J ^{− 3} × 105J

•  20,000 J − 50,000 J

•  20,000 J − 50,000 J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up ? Fat supplies 3.8×10⁷ J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g=9.8 ms⁻²:

• 2.45 ×10⁻³ kg

• 6.45 x×10⁻³ kg

• 9.89 ×10⁻³ kg

• 9.89 ×10⁻³ kg

A particle of mass 100 g is thrown vertically upwards with a speed of 5 m/s. the work done by the force of gravity during the time the particle goes up is

• 0.5 J

• -0.5 J

• −1.25 J

• −1.25 J