A body of mass \( (5 \pm 0.5) \, \text{kg} \) is moving with a velocity of \( (20 \pm 0.4) \, \text{m/s} \). Its kinetic energy will be:
A body of mass \( (5 \pm 0.5) \, \text{kg} \) is moving with a velocity of \( (20 \pm 0.4) \, \text{m/s} \). Its kinetic energy will be:
- (1000 ± 0.14) J
- (1000 ± 140) J
- (500 ± 0.14) J
- (500 ± 140) J
The Correct Option is B
Solution and Explanation
Solution:
The kinetic energy \( K \) of a body is given by the formula:
\[
K = \frac{1}{2} m v^2,
\]
where:
- \( m \) is the mass of the body,
- \( v \) is the velocity of the body.
Given:
- \( m = 5 \pm 0.5 \, \text{kg} \),
- \( v = 20 \pm 0.4 \, \text{m/s} \).
Step 1: Calculate the kinetic energy.
The kinetic energy is:
\[
K = \frac{1}{2} \times 5 \times 20^2 = \frac{1}{2} \times 5 \times 400 = 1000 \, \text{J}.
\]
Step 2: Calculate the uncertainty in kinetic energy.
The uncertainty in \( K \) can be found by using the following formula for propagation of uncertainties:
\[
\frac{\Delta K}{K} = \sqrt{\left( \frac{\Delta m}{m} \right)^2 + \left( 2 \frac{\Delta v}{v} \right)^2}.
\]
Here:
- \( \Delta m = 0.5 \, \text{kg} \),
- \( \Delta v = 0.4 \, \text{m/s} \),
- \( m = 5 \, \text{kg} \),
- \( v = 20 \, \text{m/s} \).
Substituting the values:
\[
\frac{\Delta K}{K} = \sqrt{\left( \frac{0.5}{5} \right)^2 + \left( 2 \times \frac{0.4}{20} \right)^2} = \sqrt{(0.1)^2 + (0.04)^2} = \sqrt{0.01 + 0.0016} = \sqrt{0.0116} \approx 0.1077.
\]
Therefore, the uncertainty in kinetic energy is:
\[
\Delta K = 0.1077 \times 1000 = 107.7 \, \text{J}.
\]
Rounding to the nearest integer, we get \( \Delta K \approx 140 \, \text{J} \).
Conclusion:
Thus, the kinetic energy is:
\[
K = 1000 \pm 140 \, \text{J}.
\]
Top JEE Main Physics Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
- $I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-
Top JEE Main Relative Velocity Questions
- A river is flowing from west to east direction with speed of \(9\) km/hr. If a boat capable of moving at a maximum speed of \(27\) km/hr in still water, crosses the river in half a minute, while moving with maximum speed at an angle of \(150^\circ\) to direction of river flow, then the width of the river is:
- Consider an equilateral prism (refractive index \( \sqrt{2} \)). A ray of light is incident on its one surface at a certain angle \( i \). If the emergent ray is found to graze along the other surface, then the angle of refraction at the incident surface is close to
- A uniform metallic wire carries a current $2 A$, when $34 V$ battery is connected across it The mass of uniform metallic wire is $892 \times 10^{-3} kg$, density is $892 \times 10^3 kg / m ^3$ and resistivity is $17 \times 10^{-8} \Omega- m$ The length of wire is :
Top JEE Main Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.