a body of mass 4kg is moving with a momentum of 12kg m/s it's kinetic energy 1:3 then ratio of their velocities
Ans:1:3
This make no sense to me.
To find the ratio of the velocities, we need to calculate the velocities of the body in two different situations:
Situation 1: Body moving with a momentum of 12 kg m/s
Momentum is given by the product of mass and velocity (p = mv). In this case, the momentum is 12 kg m/s and the mass is 4 kg. Therefore, we can calculate the velocity using the formula:
p = mv
12 = 4v1
v1 = 3 m/s
Situation 2: Body with kinetic energy ratio of 1:3
The kinetic energy formula is given by K = (1/2)mv^2. In this case, the kinetic energy ratio is given as 1:3. Let's assume the velocity is v2.
Since the ratio of kinetic energy is given as 1:3, we can write:
(1/2) * m * v1^2 : (1/2) * m * v2^2 = 1:3
Simplifying the equation:
v1^2 : v2^2 = 1:3
Substituting the value of v1 from Situation 1:
(3)^2 : v2^2 = 1:3
9 : v2^2 = 1:3
Cross multiplying the equation:
v2^2 = 9 * 3
v2^2 = 27
Taking the square root of both sides:
v2 = √27
v2 = 3√3 m/s
Therefore, the ratio of the velocities is:
v1 : v2 = 3 : 3√3
To simplify the ratio, we can divide both sides by 3:
v1/3 : v2/3 = 1 : √3
Hence, the ratio of their velocities is 1:√3, or in decimal form, 1:1.732.