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101.

A 100 m long train crosses a man travelling at `5 kmh^(-1)` , in opposite direction, in `7.2 s` then the velocity of train isA. 40 km/hrB. 25 km/hrC. 20 km/hrD. 45 km/hr

Answer» Correct Answer - D
Length of train L=100m
Let speed of train `=v_(1)`
and speed of man `v_(m)=5 km//hr`
relative speed `=v_(1)+v_(m)`
`v_(rel)=("Separation")/("Time")=(100)/(7.2)m//s`
`=(1000)/(72)xx(18)/(5)=50 km//hr`
`therefore v_(1)+5=50 rArr v_(1)=45 km//hr`
Discussion
102.

Assertion: The average velocity of a particle is zero in a time interval. It is possible that the instantaneous acceleration is never zero in the interval. Reason: The magnitude of average velocity in an interval is equal to its average speed in that interval.A. If both assertion `&` Reason are True `&` the Reason is a corrrect explanation of the Asserion.B. If both Assertion `&` Reason are True but Reason is not correct explanation of the Assertion.C. If Assertion is Trie but the Reason is False.D. If both Assertion `&` Reason are false

Answer» Correct Answer - C
Discussion
103.

The instantaneous speed of a body can be measured:-A. GraphicallyB. By speedometerC. Both of aboveD. Vectorially

Answer» Correct Answer - C
Discussion
104.

A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point. .A. DB. AC. BD. C

Answer» Correct Answer - D
Instantaneous velocity `=(dx)/(dt)` = slope of s-t curve.
Discussion
105.

The motion of a particle is described by the equation `x = a+bt^(2)` where `a = 15` cm and `b = 3 cm//s`. Its instantaneous velocity at time 3 sec will beA. 36 cm/secB. 18 cm/secC. 16 cm/secD. 32 cm/sec

Answer» Correct Answer - B
`x=a+bt^(2)therefore(dx)/(dt)=2bt`
at t=3 sec
`therefore` velocity =2bt`=2xx3xx3=18 cm//s`
Discussion
106.

The position `x` of a particle varies with time `t` as `x=at^(2)-bt^(3)`. The acceleration at time `t` of the particle will be equal to zero, where (t) is equal to .`A. `(2a)/(3b)`B. `(a)/(b)`C. `(a)/(3b)`D. zero

Answer» Correct Answer - C
Discussion
107.

Assertion: In general |Displacement| `le` distance. Reason: The instantaneous speed is equal to the magnitude of the instantaneous velocity,A. If both assertion `&` Reason are True `&` the Reason is a corrrect explanation of the Asserion.B. If both Assertion `&` Reason are True but Reason is not correct explanation of the Assertion.C. If Assertion is Trie but the Reason is False.D. If both Assertion `&` Reason are false

Answer» Correct Answer - B
Discussion
108.

A body is moving according to the equation `x=at+bt^(2)-ct^(3)`. Then its instantaneous speed is given By :-A. a+2B+3cB. `a+2bt-3ct^(2)`C. 2b-6ctD. None of these

Answer» Correct Answer - B
Discussion
109.

Assertion : A body can have acceleration even if its velocity is zero at a given instant of time. Reason : A body is momentarily at rest when it reverses its direction of motion.A. If both assertion `&` Reason are True `&` the Reason is a corrrect explanation of the Asserion.B. If both Assertion `&` Reason are True but Reason is not correct explanation of the Assertion.C. If Assertion is Trie but the Reason is False.D. If both Assertion `&` Reason are false

Answer» Correct Answer - A
Discussion
110.

The deceleration exerienced by a moving motor blat, after its engine is cut-off is given by `dv//dt=-kv^(3)`, where `k` is constant. If `v_(0)` is the magnitude of the velocity at cut-off, the magnitude of the velocity at a time `t` after the cut-off is.A. `(v_(0))/(2)`B. `v_(0)`C. `v_(0)e^(-k//1)`D. `(v_(0))/sqrt((2v_(0)^(2)kt+1))`

Answer» Correct Answer - D
at t=0 velocity `=v_(0)`
now `(dv)/(dt)=-kv^(2)rArr v^(-3)dv=-k dt `
Intergrating both sides
`int_(v_(0))^(v)v^(-3)dv=-kint_(0)^(t)dtrArr [(v^(-3+1))/(-3+1)]_(v_(0))^(v)=k[t]_(0)^(1)`
`-(1)/(2)[(2)/(v^(2))-(1)/(v_(0)^(2))]=-kt`
`(1)/(v^(2))=2kt+(1)/(v_(0)^(2)) rArr (1)/(v^(2))=(2kt v_(0)^(2)+1)/(v_(0)^(2))`
`v=(v_(0))/sqrt(2ktv_(0)^(2)+1)`
Discussion
111.

Let `r_(1)(t)=3t hat(i)+4t^(2)hat(j)` and `r_(2)(t)=4t^(2) hat(i)+3that(j)` represent the positions of particles 1 and 2, respectiely, as function of time t, `r_(1)(t)` and `r_(2)(t)` are in metre and t in second. The relative speed of the two particle at the instant t = 1s, will beA. 1m/sB. `3sqrt(2)m//s`C. `5sqrt(2)m//s`D. `7sqrt(2) m//s`

Answer» Correct Answer - C
Here,
`vecr_(1)(t)=3thati+4t^(2)hatj`
`vecr_(2)(t)=4t^(2)hati+3thatj`
velocity, `vecv_(1)(t)=(dvecr_(1))/(dt)=(d)/(dt)(3t hati+4t^(2)hatj)`
`=3hati+8hatj`
`vecv_(2)(t)=(dvecr_(2))/(dt)=(d)/(dt)(4t^(2)hati+3t hat j)=8t hati+3 hatj`
The relative speed of particle 1 with respect to particle 2 is
`vecv_(12)=vecv_(1)-vecv_(2)`
`=(3hati+8thatj)-(8thati+3hatj)`
`=(3-8t)hati+(8t-3)hatj`
At t=1s,
`vecv_(12)=(3-8)hati+(8-3)hatj`
`=-5hati+5hatj`
`|vecv_(12)|sqrt((-5)^(2)+(5)^(2))`
`=sqrt(25+25)=5sqrt(2) m//s`
Discussion
112.

A body X is projected upwards with a velocity of `98 ms^(-1)`, after 4s, a second body Y is also projected upwards with the same initial velocity . Two bodies will meet afterA. 6sB. 8sC. 10sD. 12s

Answer» Correct Answer - D
Let they meet after time t from projection of first at height h above the ground then
`h=ut-(1)/(2)"gt"^(2)`
for `1^(st) h=98t-(1)/(2)xx9.8xxt^(2)`
for `2^(nd) h=98(t-4)-(1)/(2)xx9.8xx(t-4)^(2)` ...(ii)
Equation (i)-(ii)
`0=98xx4+(9.8)/(2)=(-8t+16)`
`40-4t+8=0 rArr 4t=48 rArr t=12` sec
Discussion
113.

A ball is projected vertically upwards with a certain initial speed. Another ball of the same mass is projected at an angle of `60^(@)` with the vertical with the same initial speed. At highest points of their journey, the ratio of their potential energies will beA. `1:1`B. `2:1`C. `3:2`D. `4:1`

Answer» Correct Answer - D
In verticle upwards. PE=mgh
`=mg((V_(2))/(2g))=(mv^(2))/(2)`...(i)
at an angle of `60^(@)` with vertical PE=mgh
`=mg((V^(2)sin^(2)30^(@))/(2g))=(mv^(2))/(8)`....(ii)
From (i)/(ii). `((PE)_(up))/((PE)_("at" theta=60^(@)"fromvt.))=((mv^(2))/(2))/((mv^(2))/(8))=(4)/(1)`
Discussion
114.

A body is projected vertically upward from the surface of the earth, then the velocity-time graph is:-A. B. C. D.

Answer» Correct Answer - B
Discussion
115.

A motorcylcle is moving with a velocity 80km/hr ahead of a car moving with a velocity of 65 km/hr in the same direction. What is the relative velocity of the motorcyle with respect ot the car:-A. 15 km/hrB. 20 km/hrC. 25 km/hrD. 145 km/hr.

Answer» Correct Answer - A
Discussion