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:$\mathrm{}$
1. $-1$
2. $-\frac{1}{2}$
3. $\frac{1}{2}$
4. \(1\)

A block of \(1\) kg is released from a top of a smooth curve AB, and then it encounters a rough surface BC, coming to rest at C. The work done by friction is: (\(g=10\) m/s²)
           
1. \(25\) J
2. \(50\) J
3. \(-25\) J
4. \(-50\) J

The work done by all the forces (external and internal) on a system equals the change in:

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 \(10\) m. During this process, the force on the bicycle due to the road is \(200\) N is directly opposed to the motion. The work done by the cycle on the road is:
1. \(+2000\) J
2. \(-200\) J
3. zero
4. \(-20000\) J

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