If the linear momentum of the object is increased by 0.1%, then the kinetic energy is increased by
Correct answer: B. 0.2%
- A. 0.1%
- B. 0.2%
- C. 0.4%
- D. 0.01%
Explanation
The linear momentum (p) of an object is given by the formula: p = mv, where m is the mass of the object and v is its velocity. If the linear momentum is increased by 0.1%, it means the new linear momentum is 100.1% of the original linear momentum: p_new = (100.1/100)p = 1.001p. Now, let's examine the relationship between kinetic energy (KE) and linear momentum. The kinetic energy of an object can be expressed as: KE = (1/2)mv^2 where m is the mass of the object and v is its velocity. Since momentum is proportional to velocity, we can write: p_new = 1.001mv. Substituting this into the kinetic energy equation: KE_new = (1/2)(p_new/m)^2 = (1/2)(1.001mv/m)^2 = (1/2)(1.001^2)v^2 = 1.001^2 (1/2)mv^2 = 1.002(KE). Therefore, if the linear momentum of the object is increased by 0.1%, the corresponding increase in kinetic energy is approximately 0.2%, given that the mass remains constant.
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Work transfers energy when a force causes displacement, while kinetic energy, gravitational potential energy and power describe motion, position and the rate of energy transfer. The work-energy theorem links net work with change in kinetic energy, and efficiency accounts for energy losses rather than treating them as energy destruction.
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