The velocity of a bullet is reduced from 200m/s to 100m/s while travelling through a wooden block of thickness 10 cm. The retardation, assuming it to be uniform, will be

The correct option is 15x10⁴ m/s².

To find the uniform retardation of the bullet, we can use the third equation of motion:
$v^2=u^2+2as$
where:
- $u$ is the initial velocity of the bullet.
- $v$ is the final velocity of the bullet.
- $a$ is the acceleration (retardation will be the magnitude of this acceleration when it is negative).
- $s$ is the distance travelled (thickness of the wooden block).

From the given data:
- Initial velocity, $u=200\text{m/s}$
- Final velocity, $v=100\text{m/s}$
- Thickness of the block, $s=10\text{cm}=0.1\text{m}$ (since $1\text{m}=100\text{cm}$)

Substituting these values into the third equation of motion:
${\left(100\right)}^2={\left(200\right)}^2+2\cdot a\cdot 0.1$

Simplifying the terms:
$10000=40000+0.2a$

Rearranging the equation to solve for $a$:
$0.2a=10000-40000$
$0.2a=-30000$
$a=-\frac{30000}{0.2}$
$a=-150000{\text{m/s}}^2$
$a=-15\times {10}^4{\text{m/s}}^2$

The negative sign indicates that the bullet is slowing down, which is retardation.
Therefore, the magnitude of the uniform retardation is:
$\text{Retardation}=15\times {10}^4{\text{m/s}}^2$