A cyclist comes to a skidding stop in \(10~\text m\). During this process, the force on the cycle due to the road is \(200~\text N\) and is directly opposed to the motion. Work done by the road on the cycle and work done by the cycle on the road respectively are:
1. \(-2000~\text J\) and \(2000~\text J\)
2. \(2000~\text J\) and \(-2000~\text J \)
3. \(0~\text J\) and \(2000~\text J\)
4. \(-2000~\text J\) and \(0~\text J\)
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 |
A woman pushes a trunk on a railway platform which has a rough surface. She applies a force of \(100\) N over a distance of \(10\) m. Thereafter, she gets progressively tired and her applied force reduces linearly with distance to \(50\) N. The total distance through which the trunk has been moved is \(20\) m. The plot of force applied by the woman and the frictional force, which is \(50\) N versus displacement is given below. Work done by the two forces over \(20\) m are:
1. | \(1750\) J and \(-1000\) J |
2. | \(1750\) J and \(1000\) J |
3. | \(-1750\) J and \(1000\) J |
4. | \(-1750\) J and \(-1000\) J |
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 \({x=0.10~\text m}\) to \({x=2.01~\text m}\). The retarding force \(F_r\) on the block in this range is inversely proportional to \(x\) over this range,
\(\begin{aligned} {F}_{r} & =\dfrac{-{k}}{x} \text { for } 0.1<{x}<2.01 {~\text{m}} \\ & =0 \quad ~\text { for } {x}<0.1 \text{ m} \text { and } {x}>2.01 \text{ m} \end{aligned}\)
where \(k=0.5~\text{J}\). 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
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 \(\dfrac{K_B}{K_C}\) at points \({B}\) and \({C}\) is:
1. | \(1:3\) | 2. | \(3:1\) |
3. | \(1:5\) | 4. | \(5:1\) |
1. | straight line | 2. | circular |
3. | projectile | 4. | can't be determined |
To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass \(1000~\text{kg}\) moving with a speed of \(18~\text{km/h}\) on a rough road and colliding with a horizontally mounted spring of spring constant \(2.5\times 10^3~\text{N/m}\). If the coefficient of friction between road and tyre of the car, \(\mu\), to be \(0.375\). Maximum compression of the spring is:
1. \(3.5~\text{m}\)
2. \(2.0~\text{m}\)
3. \(1.5~\text{m}\)
4. \(2.5~\text{m}\)
The values of energy required to break one bond in DNA \((10^{-20}~\mathrm{J})\) and the kinetic energy of an air molecule \((10^{-21}~\mathrm{J})\) in eV respectively are:
1. | \(0.6\) eV and \(0.06\) eV |
2. | \(0.006\) eV and \(0.06\) eV |
3. | \(0.06\) eV and \(0.06\) eV |
4. | \(0.06\) eV and \(0.006\) eV |