If \(\vec{F} = (60\hat{i} + 15\hat{j}-3\hat{k})\) N and \(\vec{v} = (2\hat{i} - 4\hat{j}+5\hat{k})\) m/s, then instantaneous power is:
1. \(195\) watt
2. \(45\) watt
3. \(75\) watt
4. \(100\) watt
A ball is dropped from a height of \(5\) m. If it rebounds up to a height of \(1.8\) m, then the ratio of velocities of the ball after and before the rebound will be:
1.
2.
3.
4.
A force \(F\) acting on an object varies with distance \(x\) as shown below:
The force is in Newton and \(x\) is in meters. The work done by the force in moving the object from \(x = 0\) to \(x = 6\) m is:
1. | \(18.0\) J | 2. | \(13.5\) J |
3. | \(4.5\) J | 4. | \(9.0\) J |
A ball is thrown vertically upward. It has a speed of 10m/sec when it has reached one-half of its maximum height. How high does the ball rise? Take g = 10 m/s2:
1. 5m
2. 15m
3. 10 m
4. 20 m
The kinetic energy of a person is just half of the kinetic energy of a boy whose mass is just half of that person. If the person increases his speed by \(1~\text{m/s},\) then his kinetic energy equals to that of the boy, then the initial speed of the person was:
1. \(\left( \sqrt{2}+1 \right)~\text{m/s}\)
2. \(\left( 2+\sqrt{2} \right)~\text{m/s}\)
3. \(2\left( 2+\sqrt{2} \right)~\text{m/s}\)
4. none of the above
A particle of mass m1 is moving with a velocity v1 and another particle of mass m2 is moving with a velocity v2. Both of them have the same momentum, but their kinetic energies are E1 and E2 respectively. If m1 > m2 then:
1.
2.
3.
4.
A stone is tied to a string of length 'l' is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed 'u'. The magnitude of the change in velocity as it reaches a position where the string is horizontal (g being acceleration due to gravity) is:
1.
2.
3.
4.
A mass of \(0.5\) kg moving with a speed of \(1.5\) m/s on a horizontal smooth surface, collides with a nearly weightless spring with force constant \(k=50\) N/m. The maximum compression of the spring would be:
1. \(0.12\) m
2. \(1.5\) m
3. \(0.5\) m
4. \(0.15\) m
A particle projected with velocity 'u' makes an angle θ with respect to horizontal. Now it breaks in two identical parts at highest point of trajectory. If one part retraces its path, then velocity of the other part is:
1. 3u cos θ
2. 2u cos θ
3. u cos θ
4. u
If two springs, A and B are stretched by the same suspended weights, then the ratio of work done in stretching is equal to:
1. 1 : 2
2. 2 : 1
3. 1 : 1
4. 1 : 4