If the kinetic energy of a body moving with a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The kinetic energy $(K)$ of a body is given by the formula $K = \frac{1}{2}mv^2$, where $m$ is the mass and $v$ is the magnitude of the velocity.F

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(D) The kinetic energy $(K)$ of a body is given by the formula $K = \frac{1}{2}mv^2$, where $m$ is the mass and $v$ is the magnitude of the velocity.First, calculate the magnitude of the velocity vector $\vec{v} = (2 \hat{i} + 3 \hat{j} - 4 \hat{k}) 	ext{ m/s}$.$v = |\vec{v}| = \sqrt{2^2 + 3^2 + (-4)^2} = \sqrt{4 + 9 + 16} = \sqrt{29} 	ext{ m/s}$.Thus, $v^2 = 29 	ext{ m}^2/	ext{s}^2$.Given $K = 87 	ext{ J}$, substitute the values into the kinetic energy formula:$87 = \frac{1}{2} 	imes m 	imes 29$.$87 = 14.5 	imes m$.$m = \frac{87}{14.5} = 6 	ext{ kg}$.Therefore, the mass of the body is $6 	ext{ kg}$.

If the kinetic energy of a body moving with a velocity of $(2 \hat{i} + 3 \hat{j} - 4 \hat{k}) \text{ m/s}$ is $87 \text{ J}$, then the mass of the body is: (in $\text{ kg}$)

Similar Questions

Two bodies of masses $m$ and $2m$ have the same momentum. Their respective kinetic energies $E_1$ and $E_2$ are in the ratio:

What is the shape of the graph between the speed and kinetic energy of a body?

Two bodies of masses $1 \,g$ and $4 \,g$ are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is

If momentum is increased by $20 \%$,then kinetic energy increases by (in $\%$)

In the Olympic games,an athlete covers a distance of $100 \ m$ in $10 \ s$. The estimated range of their kinetic energy is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module