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**Objective Questions (Level 1) ****Single Correct Option****Ques 1: A packet is released from a rising balloon accelerating upward with acceleration a. The acceleration of the stone just after the release is ****(a) a upward ****(b) g downward ****(c) (g - a) downward ****(d) (g + a) downward****Ans: **g downward**Sol: **As the packet is detached from rising balloon its acceleration will be g in the downward direction.

Option (b) is correct.**Ques 2: A ball is thrown vertically upwards from the ground. If T _{1} and T_{2} are the respective time taken in going up and coming down, and the air resistance is not ignored, then **

Using v

i.e.,

While coming down

â‡’

Using Eq. (i) and Eq. (ii)

â‡’ T

Option (c) is correct.

Speed of the tip of seconds hand

As in 15s the seconds hand rotates through 90Â°, the change in velocity of its tip in 15 s will be

Option (d) is correct.

Option (c) is correct.

Option (b) is correct.

**Ques 7: A particle moves along a straight line. Its position at any instant is given by where x is in metre and t in second. Find the acceleration of the particle at the instant when particle is at rest, ****(a) -16 ms ^{-2} **

** â€¦(i)**

âˆ´ Particle is at rest when

32 - 8 t^{2} = 0

i.e., t = 2 s

Differentiating Eq. (i) w.r.t. time t

âˆ´ a at time t = 2 s (when particle is at rest)

= - (16) x (2) = -32 m/s^{2}

Option (b) is correct.**Ques 8: A car starts from rest and accelerates at constant rate in a straight line. In the first second the car covers a distance of 2 m. The velocity of the car at the end of second (sec) will be ****(a) 4.0 ms ^{-1 }**

â‡’ a = 4 m/s

Velocity at the end of next second

v = (4) x (2) = 8 m/s

Option (b) is correct.

âˆ´ displacement at time t (= 1 s)

= - 3(1) + (1)

and displacement at time t (= 3 s)

= - 3(3) + (3)

And as such displacement in the time interval (t = 1 s to t = 3 s)

= (18 m) - (- 2 m)

= + 20 m

Option (c) is correct.

âˆ´ C = v

i.e.,

or

or

or

At t = 0, s = 0,

âˆ´ k = 0

â‡’

Option (a) is correct.

âˆ´

âˆ´ Height of 2nd drop from ground

Option (c) is correct.

[At time = t - 1]

or t

or 2t - 3 = 0

or

âˆ´

= 11.25 m

Option (c) is correct.

(b) 3 v

(c) 9 v

(d) 3/2 v

âˆ´

or u = v

Option (a) is correct.

(b) x = y

(c) x = y

(d) None of these

âˆ´

or âˆ« dx = âˆ« (8 t - 2) dt

or x = 4t

Now at t = 2, x = 14

âˆ´ 14 = 4 Ã— 2

i.e., k

Thus, x = 4 t

Further, v

i.e.,

or âˆ« dy = âˆ« 2 dt

or y = 2t + k

Now, at t = 2, y = 4

âˆ´ k

Thus, y = 2t â€¦(ii)

Substituting t = y/2 in Eq. (i),

or x = y

Option (a) is correct.

âˆ´

Now,

â‡’ t = 1 s

Option (b) is correct.

âˆ´

At t = 0

âˆ´ Velocity of projection

Option (c) is correct.

âˆ´

Option (c) is correct.

= a + a + a = 3 a

âˆ´ Time taken = 3a/u

Option (a) is correct.

(b) 64 m

(c) 32 m

(d) 36 m

âˆ´ Height of lift above the starting point when it comes to rest

= Area under t-v graph

Option (b) is correct.

In time interval t

In time interval t

âˆ´

i.e., t

Now t

âˆ´ 2t

or t

Depth of shaft = Displacement of lift

Option (b) is correct.

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