Question:
A new unit (\(\alpha\)) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of \(\alpha\) units if light takes 6 min. 40 s to cover this distance?
A new unit (\(\alpha\)) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of \(\alpha\) units if light takes 6 min. 40 s to cover this distance?
Updated On: Apr 13, 2026
- 200 \(\alpha\)
- 400 \(\alpha\)
- 300 \(\alpha\)
- 500 \(\alpha\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
Distance is defined as the product of speed and time. In this problem, the unit of length is redefined based on the speed of light. We need to convert the travel time into seconds to find the total distance in the new unit system.
Step 2: Key Formula or Approach:
1. Distance \(d = v \times t\).
2. New unit of length \(1 \alpha = c \times (1 \text{ second})\), where \(c\) is the speed of light.
Step 3: Detailed Explanation:
The given time is 6 minutes and 40 seconds. \[ t = (6 \times 60) + 40 = 360 + 40 = 400 \text{ seconds} \] The distance covered by light in vacuum is: \[ d = c \times t = c \times 400 \] Since the new unit \(\alpha\) is numerically equal to the speed of light \(c\) (meaning 1 unit of \(\alpha\) is the distance light travels in 1 second), the distance becomes: \[ d = 400 \alpha \]
Step 4: Final Answer:
The distance between Venus and Earth is 400 \(\alpha\) units.
Distance is defined as the product of speed and time. In this problem, the unit of length is redefined based on the speed of light. We need to convert the travel time into seconds to find the total distance in the new unit system.
Step 2: Key Formula or Approach:
1. Distance \(d = v \times t\).
2. New unit of length \(1 \alpha = c \times (1 \text{ second})\), where \(c\) is the speed of light.
Step 3: Detailed Explanation:
The given time is 6 minutes and 40 seconds. \[ t = (6 \times 60) + 40 = 360 + 40 = 400 \text{ seconds} \] The distance covered by light in vacuum is: \[ d = c \times t = c \times 400 \] Since the new unit \(\alpha\) is numerically equal to the speed of light \(c\) (meaning 1 unit of \(\alpha\) is the distance light travels in 1 second), the distance becomes: \[ d = 400 \alpha \]
Step 4: Final Answer:
The distance between Venus and Earth is 400 \(\alpha\) units.
Was this answer helpful?
0
0
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:-
View More Questions
Top JEE Main Units, Dimensions and Measurements Questions
- Match List-I with List-II.
- Find the dimension of \( \frac{E}{B} \) where, E represents electric field and B represents magnetic field.
- Which of the following quantity has the same dimensions as \( \sqrt{\frac{\mu_0}{\epsilon_0}} \)?
- A fractional errors in $x$, $y$, and $z$ are $0.1$, $0.2$, and $0.5$ respectively. Find the maximum fractional error in $x^{-2} y^3 z^{-2}$.
- Match the columns:
View More Questions
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 ______.
View More Questions