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The rate of change of momentum with respect to time is measured in
- a)kg ms-2
- b)kg ms-1
- c)kg m
- d)kg
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The rate of change of momentum with respect to time is measured ina)kg...
We know, p = mv
Units of p, ⇒ kg ms-1
We have to measure, rate of change of momentum with respect to time ;
⇒ kg m s-2
Units of p, ⇒ kg ms-1
We have to measure, rate of change of momentum with respect to time ;
⇒ kg m s-2
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The rate of change of momentum with respect to time is measured ina)kg...
Rate of change of momentum:
The rate of change of momentum is the derivative of momentum with respect to time. Momentum is defined as the product of mass and velocity of an object. Therefore, the rate of change of momentum can be expressed as:
dP/dt = d(mv)/dt
where P is the momentum, m is the mass, and v is the velocity.
Units of rate of change of momentum:
The units of momentum are kg m/s. Therefore, the units of rate of change of momentum can be derived by taking the derivative of momentum with respect to time. The derivative of momentum with respect to time is:
dP/dt = d(mv)/dt = m(dv/dt) + v(dm/dt)
The first term on the right-hand side of the equation represents the rate of change of velocity with respect to time, which is acceleration. The units of acceleration are m/s^2. The second term represents the rate of change of mass with respect to time, which is not usually considered in most cases. Therefore, the units of rate of change of momentum are:
dP/dt = m(dv/dt) + v(dm/dt) = kg m/s^2 = N (newton)
However, Newton's second law of motion states that force is equal to the rate of change of momentum. Therefore, the units of force can also be expressed as kg m/s^2 or N.
The rate of change of momentum is the derivative of momentum with respect to time. Momentum is defined as the product of mass and velocity of an object. Therefore, the rate of change of momentum can be expressed as:
dP/dt = d(mv)/dt
where P is the momentum, m is the mass, and v is the velocity.
Units of rate of change of momentum:
The units of momentum are kg m/s. Therefore, the units of rate of change of momentum can be derived by taking the derivative of momentum with respect to time. The derivative of momentum with respect to time is:
dP/dt = d(mv)/dt = m(dv/dt) + v(dm/dt)
The first term on the right-hand side of the equation represents the rate of change of velocity with respect to time, which is acceleration. The units of acceleration are m/s^2. The second term represents the rate of change of mass with respect to time, which is not usually considered in most cases. Therefore, the units of rate of change of momentum are:
dP/dt = m(dv/dt) + v(dm/dt) = kg m/s^2 = N (newton)
However, Newton's second law of motion states that force is equal to the rate of change of momentum. Therefore, the units of force can also be expressed as kg m/s^2 or N.
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