If a vector $2\hat{i}+3\hat{j}+8\hat{k}$ is perpendicular to the vector $-4\hat{i}+4\hat{j}+\alpha \hat{k},$ then the value of $\alpha$ will be:
1. $-1$
2. $\frac{-1}{2}$
3. $\frac{1}{2}$ 
4. $1$

A block of $1$ kg is released from the top of a smooth curve $\mathrm{AB},$ and then it encounters a rough surface $\mathrm{BC},$ coming to rest at $\mathrm{C}.$ The work done by friction is:
(take $g=10$ m/s²)

The work done by all the forces (external and internal) on a system equals the change in:
1. total energy
2. kinetic energy
3. potential energy
4. none of these

A body of mass $1$ kg is thrown upwards with a velocity $20$ ms^-1. It momentarily comes to rest after attaining a height of $18$ m. How much energy is lost due to air friction?
(Take $g=10$ ms^-2)
1. $20$ J
2. $30$ J
3. $40$ J
4. $10$ J

A bicyclist comes to a skidding stop in $10~\text m.$ During this process, the force on the bicycle due to the road is $200~\text N$ is directly opposed to the motion. The work done by the cycle on the road is:
1. $+2000~\text J$
2. $-200~\text J$
3. zero
4. $-20000~\text J$

A body of mass $0.5~\text{kg}$ travels in a straight line with velocity $v=ax^{3/2}$ where $a=5~\text{m}^{-1/2}\text{s}^{-1}$. The work done by the net force during its displacement from $x=0~\text{m}$ to $x=2~\text{m}$ is:
1. $15~\text{J}$
2. $50~\text{J}$
3. $10~\text{J}$
4. $100~\text{J}$