Chapter 6, Problem 3STP

To determine

To Choose: The correct option.

Answer to Problem 3STP

Option B. $3.1\text{m/s}$

Explanation of Solution

Given:

The force exerted by a 2m massless string on a 0.82kg object swinging in a horizontal circle is 4.0N.

Formula used:

The centripetal force acting on an object is given by:

  $F=m{a}_c$

Where, $a_c=\frac{v^2}{r}$ is the centripetal acceleration, $v$ is the velocity of the object and r is the radius.

Calculation:

Now, since the object is whirling in a horizontal circle, the force exerted on it is balanced by the centripetal force as:

  $F=F_c=m{a}_c=\frac{m{v}^2}{r}$

Substitute the given values in the above equation;

  $\begin{array}{c}4=\frac{0.82v^2}{2.0}\\ v=3.1\text{m/s}\end{array}$

Conclusion:

Thus, tangential velocity of the object is $3.1\text{m/s}$ .