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1.

A train accelerating uniormly from rest attains a maximum speed of `40ms^(-1)` in `20s`. It travels at this speed for `20s` and is brought to rest with uniform retardation i further `40s`. What is the average velocity during this period?A. `80m//s`B. `25m//s`C. `40 m//s`D. `30m//s`

Answer» (b) (i) `v=u=at_(1)`
`40=0+axx20`
`a=2m//s^(2)`
`v^(2)-u^(2)=2as`
`40^(@)-0=2xx2s_(1)`
`:. s_(1)=400m`
(ii) `s_(2)=vxxt_(2)=40xx220=800m`
(iii) `v=u+at`
`0=40+axx40`
`:. a=-1m//s^(2)`
`0^(2)=40^(2)=2(-1)s_(3)`
`:. s_(3)=800m`
Total distance travelled `=s_(1)+s_(2)+s_(3)`
`=400+800+800=2000m`
Total time taken `=20+20+40=80s`
`:.` Average velocity `=2000/80`
`=25m//s`
Discussion
2.

A body moves with uniform acceleration, which of the following graph is correct?A. B. C. D.

Answer» (c) An object is said to be moving with a uniform acceleration if its velocity changes by equal amount in equal intervals of time. The velocity time graph of uniformly accelerated motion is straight line inclined to time axis. Acceleration of an object in a uniformly accelerated motion in one dimension is equal to the slope of the velocity time graph with time axis.
Discussion
3.

Two particles start from the same point with different speeds but one moves along `y=a sin omega x` and other moves along curve `y=cos omegax`A. they must collide after some timeB. they never collide with each otherC. they may collide at the point `P((pi)/(4omega),a/(sqrt(2)))`D. they must collide at the point `P`

Answer» Correct Answer - (C)
Discussion
4.

A person travelling on a straight line moves with a uniform velocity `v_1` for some time and with uniform velocity `v_2` for the next equal time. The average velocity v is given byA. `v=(v_(1)+v_(2))/2`B. `2/v=1/(v_(1))+1/(v_(2))`C. `v=sqrt(v_(1)v_(2))`D. `1/v=1/(v_(1))=1/(v_(2))`

Answer» Correct Answer - (a)
Discussion
5.

For a man who wants to cross the river, with the shortest path `AB`, find the anglet `theta` (see figure) A. `sin^(-1)(3/4)`B. `sin^(-1)(4/3)`C. `30^(@)`D. Given situation is not possible

Answer» (d) For the man to cross the river frm the shortest path,
`V_(m) sin theta=v_(r)`
`sin theta=(v_(r))/(v_(m))`
`sin theta=4/3`
`theta =sin^(-1)(/3)`
But it is not possible, because `sin theta` could not be greater than `t`. Hence the man could not cross the river from the shortest path `AB`.
Discussion
6.

Do we observe the time variation of position is nature as shown in the graph? A. yesB. noC. oftenD. Rarely

Answer» (b) As `x` increases, time first increases and then decreases. This not possible.
Discussion
7.

Rain water is falling vertically downward with velocity `v`. When velocity of wind is `u` in horizontal direction, water is collected at the rate of `R m^(3)//s`. When velocity of wind becomes `2u` in horizontal direction. The rate of collection of water in vessel isA. `R`B. `R/2`C. `2R`D. `(Rsqrt(4u^(2)+v^(2)))/(sqrt(u^(2)+v^(2)))`

Answer» (a) The rate of storing water in vessel depends upon vertical component of velocity in this problem vertical component of velocity in both cases are same.
Discussion
8.

Rain drops fall vertically at a speed of `20m//s`. At what angle do they fall on the wind screen of a car moving with a velocity of `15m//`, if the wind screen velocity incined at an agle of `23^(@)` to the vertical `("cot"^(-1)4/3~~37^(@))`A. `60^(@)`B. `30^(@)`C. `45^(@)`D. `90^(@)`

Answer» (a) `tan (90^(@)-theta)=20/15`
`:. cot theta=20/15=4/3`
`impliestheta=37^(@)`
`:. alpha=37^(@)+23^(@)=60^(@)`
Discussion
9.

Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to the initial horizontal velocity component, highest first. .A. `1,2,3,4`B. `2,3,4,1`C. `3,4,1,2`D. `4,3,2,1`

Answer» Correct Answer - (d)
Discussion