**Problem:**A 1000-kg car is revolving uniformly in a horizontal circle of radius 10 m with a speed of 0.5 m/s. Calculate its centripetal acceleration.**Options:**- A. 50 m/s$^2$- B. 0.025 m/s$^2$- C. 0.25 m/s$^2$- D. 0.5 m/s$^2$**Explanation:**The problem presents a situation where we need to find the centripetal acceleration of a car moving in a circular path. The formula for centripetal acceleration $a_c$ is given by:\[ a_c = \frac{v^2}{r} \]where:- $v$ is the speed of the car (0.5 m/s),- $r$ is the radius of the circle (10 m).By calculating using the formula, you can determine the correct option for the centripetal acceleration.

Answered: A 1000-kg car is revolving uniformly in…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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**Problem:**

A 1000-kg car is revolving uniformly in a horizontal circle of radius 10 m with a speed of 0.5 m/s. Calculate its centripetal acceleration.

**Options:**

- A. 50 m/s$^2$
- B. 0.025 m/s$^2$
- C. 0.25 m/s$^2$
- D. 0.5 m/s$^2$

**Explanation:**

The problem presents a situation where we need to find the centripetal acceleration of a car moving in a circular path. The formula for centripetal acceleration $a_c$ is given by:

\[ a_c = \frac{v^2}{r} \]

where:
- $v$ is the speed of the car (0.5 m/s),
- $r$ is the radius of the circle (10 m).

By calculating using the formula, you can determine the correct option for the centripetal acceleration.

Expert Solution

Step 1

When a body move in a circular path with constant speed then its direction changes continuous. Due to this velocity changes. The circular motion of the body due a force called centripetal force, acting toward the center of circle.

Hence an acceleration work on the body which direction is toward the center of circle, this acceleration is known as centripetal acceleration.

Centripetal force acting on the body is given by

$F = \frac{m v^{2}}{r}$

hence centripetal acceleration is given by

$a = \frac{F}{m} = \frac{v^{2}}{r}$

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