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:  Work Energy Theorem |
 66%
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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:  Work Energy Theorem |
 56%
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A bob of mass m is suspended by a light string of length L. It is imparted a horizontal velocity v0 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 v0 is:

1.   5gl

2.   4gl

3.  3gl

4.   gl

Subtopic:  Work Energy Theorem |
 66%
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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 \(\frac{K_B}{K_C}\) at points \(\mathrm{B}\) and \(\mathrm{C}\) is:

                  
1. \(1:3\)
2. \(3:1\)
3. \(1:5\)
4. \(5:1\)

Subtopic:  Work Energy Theorem |
 77%
From NCERT
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A bob of mass m is suspended by a light string of length L. It is imparted a horizontal velocity v0 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:  Work Energy Theorem |
 63%
From NCERT
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In a nuclear reactor, a neutron of high speed (typically 107 m/s) must be slowed to 103 m/s so that it can have a high probability of interacting with isotope U92235 and causing it to fission. The material making up the light nuclei, usually heavy water D2O 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.  19

2.  89

3.  98

4.  18

Subtopic:  Work Energy Theorem |
 67%
From NCERT
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