In a ballistics demonstration, a police officer fires a bullet of mass $$50.0$$ g with speed $$200$$ m/s on soft plywood of thickness $$2.00$$ cm. The bullet emerges with only $$\text{10%}$$ of its initial kinetic energy. The emergent speed of the bullet is:
1. $$0$$
2. $$53.2$$ m/s
3. $$63.2$$ m/s
4. $$6.32$$ m/s

Subtopic: Â Work Energy Theorem |
Â 66%
From NCERT
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

A block of mass $$m=1$$ kg, moving on a horizontal surface with speed $$v_i=\mathrm{2~m/s}$$ enters a rough patch ranging from $$\mathrm{x=0.10~m}$$ to $$\mathrm{x=2.01~m}$$. The retarding force $$F_r$$ on the block in this range is inversely proportional to $$x$$ over this range,
\begin{aligned} \mathrm{F}_{\mathrm{r}} & =\frac{-\mathrm{k}}{\mathrm{x}} \text { for } 0.1<\mathrm{x}<2.01 \mathrm{~m} \\ & =0 \quad \text { for } \mathrm{x}<0.1 \mathrm{~m} \text { and } \mathrm{x}>2.01 \mathrm{~m} \end{aligned}
where $$k=0.5~\mathrm{J}$$. What is the final kinetic energy and speed $$v_f$$ of the block as it crosses this patch?
1. 5 J and 1 m/s
2. 1 J and 5 m/s
3. 0.5 J and 1 m/s
4. 0.05 J and 2 m/s

Subtopic: Â Work Energy Theorem |
Â 56%
From NCERT
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

A bob of mass m is suspended by a light string of length L. It is imparted a horizontal velocity ${\mathrm{v}}_{0}$ at the lowest point A such that it completes a semi-circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point, the horizontal velocity ${\mathrm{v}}_{0}$ is:

1.   $\sqrt{5\mathrm{gl}}$

2.   $\sqrt{4\mathrm{gl}}$

3.  $\sqrt{3\mathrm{gl}}$

4.   $\sqrt{\mathrm{gl}}$

Subtopic: Â Work Energy Theorem |
Â 66%
From NCERT
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

A bob of mass m is suspended by a light string of length $$L.$$ It is imparted a horizontal velocity $$v_0$$ at the lowest point A such that it completes a semi-circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point, the ratio of the kinetic energies $$\frac{K_B}{K_C}$$ ${\mathrm{}}_{}$at points $$\mathrm{B}$$ and $$\mathrm{C}$$ is:
${\mathrm{}}_{}$

1. $$1:3$$
2. $$3:1$$
3. $$1:5$$
4. $$5:1$$

Subtopic: Â Work Energy Theorem |
Â 77%
From NCERT
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

A bob of mass m is suspended by a light string of length L. It is imparted a horizontal velocity ${\mathrm{v}}_{0}$ at the lowest point A such that it completes a semi-circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point. If the connecting string is cut at point C, the trajectory of bob is:

1.   Straight line

2.   Circular

3.   Projectile

4.   Can't be determined

Subtopic: Â Work Energy Theorem |
Â 63%
From NCERT
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

In a nuclear reactor, a neutron of high speed (typically ${10}^{7}$ m/s) must be slowed to ${10}^{3}$ m/s so that it can have a high probability of interacting with isotope ${}_{92}{}^{235}\mathrm{U}$ and causing it to fission. The material making up the light nuclei, usually heavy water $\left({\mathrm{D}}_{2}\mathrm{O}\right)$ or graphite, is called a moderator. Find the fraction of the kinetic energy of the neutron lost by it in an elastic collision with light nuclei like deuterium.

1.  $\frac{1}{9}$

2.  $\frac{8}{9}$

3.  $\frac{9}{8}$

4.  $\frac{1}{8}$

Subtopic: Â Work Energy Theorem |
Â 67%
From NCERT
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints