Relative Velocity

Q. A bus is beginning to move with an acceleration of $1{\text{m/s}}^2$. A boy who is $48\text{m}$ behind the bus starts running with constant speed of $10\text{m/s}$. The earliest time when the boy can catch the bus is

1. 10 sec
2. 8 sec
3. 12 sec
4. 14 sec

Q.

A person standing on an open ground hears the sound of a jet aeroplane, coming from the north at an angle ${60}^0$ with ground level. But he finds the aeroplane right vertically above his position. If $v$ is the speed of sound, the speed of the plane is

1. $\left(\raisebox{1ex}{$\sqrt{3}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)v$

2. $\raisebox{1ex}{$2v$}\!\left/ \!\raisebox{-1ex}{$\sqrt{3}$}\right.$

3. $V$

4. $\raisebox{1ex}{$v$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

Q.

What did Einstein mean by time is relative?

Q.

What is the relation between escape and orbital velocity?

Q.

A block of metal weighing 2 Kg is resting on a frictionless plane. It is struck by a jet releasing water at a rate of 1 $kg{s}^{-1}$and at a speed of 5 $m{s}^{-1}$. The initial acceleration of the block is

1. 

2. 

3. 

4. 

Q. A bus starts moving with acceleration $2{\text{ms}}^{-2}$. A cyclist $96\text{m}$ behind the bus starts simultaneously towards the bus at a constant speed of $20\text{m/s}$. After what time will he be able to overtake the bus?

1. $4\text{s}$
2. $8\text{s}$
3. $12\text{s}$
4. $16\text{s}$

Q. A motorboat covers a given distance in $6\text{hours}$ moving downstream in a river. It covers the same distance in $10\text{hours}$ moving upstream. The time taken to cover the same distance in still water is

1. $9\text{hours}$
2. $7.5\text{hours}$
3. $6.5\text{hours}$
4. $8\text{hours}$

Q.

Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity$v_1$. The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is

1. 
2. 
3. 
4. 

Q. A boat is sent across a river with a velocity of 8 km/hr. If the resultant velocity of boat is 10 km/hr, then velocity of the river is :

1. 10 km/hr
2. 8 km/hr
3. 6 km/hr
4. 4 km/hr

Q. Two cars are moving in the same direction with a speed of $30\text{kmph}$. They are seperated from each other by $5\text{km}$. Third car moving in the opposite direction meets the two cars after an interval of 4 minutes. What is the speed of the third car?

1. $35\text{kmph}$
2. $30\text{kmph}$
3. $40\text{kmph}$
4. $45\text{kmph}$

Q.

Suppose while sitting in a parked car, you notice a jogger approaching towards you in the side view mirror of R= 2m. If the jogger is running at a speed of 5ms^-1 , how fast the image of the jogger appear to move when the jogger is 39m away?

Q. A man moving at speed of $5\text{m/s}$ observes rain falling vertically with velocity $5\sqrt{3}m/s$. Find the speed and direction of the rain w.r.t ground.

1. $5\text{m/s}$, ${60}^{\circ }$ with vertical
2. $10\text{m/s}$, ${60}^{\circ }$ with vertical
3. $10\text{m/s}$, ${30}^{\circ }$ with vertical
4. $5\text{m/s}$, ${30}^{\circ }$ with vertical

Q.

LED is constructed from Ga-As-P semiconducting material. The energy gap of this LED is$1.9eV$. Calculate the wavelength of light emitted and its color.$[\mathrm{h}=6.63\times {10}^{-34}\mathrm{Js}\mathrm{and}\mathrm{c}=3\times {10}^8{\mathrm{ms}}^{-1}]$

1. $654nm$and red color

2. $1046nm$ and blue color

3. $1046nm$ and red color

4. $654nm$ and orange color

Q. A 100 m long train is moving with a uniform velocity of 45 km/hr. The time taken by the train to cross a bridge of length 1 km is

1. 88 s
2. 58 s
3. 68 s
4. 78 s

Q.

A tunnel is dug along a chord of the earth at a perpendicular distance $\frac{R}{2}$ From the earth's centre. The wall of the tunnel may be assumed to be frictionless. Find the force exerted by the wall on a particle of mass m when it is at a distance x from the centre of the tunnel.

Q. The distance between two stars of masses $3M_S$ and $6M_S$ is $9R$. Here $R$ is the mean distance between the centers of the Earth and the Sun, and $M_S$ is the mass of the Sun. The two stars orbit around their common center of mass in circular orbits with period $nT$, where $T$ is the period of Earth’s revolution around the Sun. The value of $n$ is

Q.

A ball is dropped from the top of a building. The ball takes 0.5sec to fall past the 3m height of a window some distance from the top of the building. If the speed of the ball at top and the bottom is vb and vt, the establish a relationship between vb and vt take (g = 9.8m/s).

Q. A ship is travelling due east at $10\text{km/hr}$. Another ship heading ${30}^{\circ }$ east of north is always due north from the first ship. The speed of the second ship in $\text{km/hr}$ is

1. $20\sqrt{2}$
2. $20\sqrt{\frac{3}{2}}$
3. $20$
4. $\frac{20}{\sqrt{2}}$

Q. A police jeep is chasing with, velocity of 45 km/h a thief in another jeep moving with velocity 153 km/h. Police fires a bullet with muzzle velocity of 180 m/s. The velocity it will strike the car of the thief is

1. 450 m/s
2. 150 m/s
3. 250 m/s
4. 27 m/s

Q. A ball is dropped from the top of a building of height 80m. At same instant another ball is thrown upwards with speed 50m/s from the bottom of the building. The time at which balls will meet is ?

Q.

A rocket is launched normal to the surface of the Earth, away from the Sun, along the line, joining the Sun and the Earth. The Sun is $3\times {10}^5$ times heavier than the Earth and is at a distance $2.5\times {10}^4$ times larger than the radius of the Earth. The escape velocity from Earth's gravitational field is $v_e=11.2km/s$. The minimum initial velocity $\left(v_s\right)$ required for the rocket to be able to leave the Sun-Earth system is closest to $($Ignore the rotation and revolution of the Earth and the presence of any other planet$)$

1. $v_s=62km/s$

2. $v_s=42km/s$

3. $v_s=72km/s$
4. $v_s=22km/s$

Q. Two trains are moving on parallel tracks in opposite directions at the speeds of $20\text{m/s}$ and $15\text{m/s}$ respectively. If both the trains are of equal length $140\text{m}$ each, then how much time will they take to cross each other?

1. $4\text{s}$
2. $8\text{s}$
3. $16\text{s}$
4. $2\text{s}$

Q. When a ceiling fan is switched off its angular velocity reduces to 50% while it makes 36 rotations. How many more rotation will it make before coming to rest (Assume uniform angular retardation)

1. 18
2. 12
3. 36
4. 48

Q. Four particles A, B, C and D are situated at the vertices of a square of side 'a' at t = 0. Each of the particles move with a constant speed 'v' such that A aims towards B, B aims towards C, C aims towards D and D aims towards A, then

1. Particles will meat at center of square at $t=\frac{\sqrt{2}a}{v}$
2. Particles will meat at center of square at $t=\frac{a}{v}$
3. Distance travelled by any particle before meeting at center is $vt$
4. Speed of approach of A and B is $\sqrt{2}v$

Q. Two trains, each $50\text{m}$ long are moving parallel towards each other at speeds $10\text{m/s}$ and $15\text{m/s}$ respectively. How much time will they take to pass each other?

1. 8s
2. 4s
3. 2s
4. 6s

Q. A thief is running away on a straight road in a jeep moving with a speed of $9{\text{ms}}^{-1}$. A policeman chases him on a motor cycle moving at a speed of $10{\text{ms}}^{-1}$. If the instantaneous separation of the jeep from the motor cycle is $100\text{m}$, how long will it take for the policeman to catch the thief?

1. $1\text{s}$
2. $90\text{s}$
3. $100\text{s}$
4. $19\text{s}$

Q.

A particle has position vector ( 3i - j + 2k) metre at t=0. It moves with constant velocity (-i + j - 3k) m/s. The position vector after 3s

Q. A body is projected vertically upward . if t1 and t2 be the times at which it is at height h above the point of projection while ascending and descending . what is the height h and the velocity of projection ?

Q. A $100\text{m}$ long train crosses a man travelling at $5\text{km/h}$ in the opposite direction in $7.2\text{s}$. Then the velocity of train is

1. $40\text{km/h}$
2. $25\text{km/h}$
3. $20\text{km/h}$
4. $45\text{km/h}$

Q. A solid cylinder attached to horizontal massless spring can roll without slipping along horizontal surface. Find time period of oscillation.

1. $2\pi \sqrt{\frac{M}{2k}}$
2. $\pi \sqrt{\frac{3M}{2k}}$
3. $\pi \sqrt{\frac{2M}{3k}}$
4. $2\pi \sqrt{\frac{3M}{2k}}$