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# Motion in Straight Line

#### Multiple Choice Questions

11.

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

• 150 m/s

• 27 m/s

• 450 m/s

• 250 m/s

A.

150 m/s

Relative velocity is the vector difference between the velocities of two bodies, the velocity of a body with respect to another regarded as being at rest.

Here, we calculate the relative velocity of the jeep:

153 -45 =108 km/h

Therefore, striking speed = relative speed of a bullet with respect to the thief's car:

180 - 30 = 150 m/s

12.

A stone is thrown with an initial speed of 4.9m/s from a bridge in vertically upward direction.It falls down in water after 2sec. The height of bridge is

• 24.7m

• 19.8 m

• 9.8 m

• 4.9 m

C.

9.8 m

Here :- Initial velocity u=-4.9m/s (-ve is due to vertically upward motion)

Total time t = 2sec

The height of the bridge is given by

s =ut+$\frac{1}{2}{\mathrm{at}}^{2}$

Here we consider a=g$⇒$acceleration due to gravity

13.

A ball of mass 10 g moving with acceleration of 20 m/s2 is hit by a force which acts on it for 0.1 sec. The impulsive force is

• 1.2Ns

• 0.3Ns

• 0.1Ns

• 0.5Ns

B.

0.3Ns

Here:- Mass of the ball m= 10 g ; time dt =0.1 sec ;

acceleration of the ball = 20m/s2

Force F =ma =0.15×20 =3N

Impulsive forces are forces that act over short times producing rapid changes in motion

$⇒$ Impulsive force = F×dt = 3×0.1 =0.3 Ns

14.

A person is standing in an elevator. In which situation he finds his weight less?

• When the elevator moves upward with constant acceleration

• when the elevator moves downward with constant acceleration

• when the elevator moves upward with uniform velocity

• When the elevator moves downward with uniform velocity

B.

when the elevator moves downward with constant acceleration

When elevator moves downward with constant acceleration.

$\mathrm{\alpha }$ = g.

Then person standing in an elevator find himself weightless.

(g' with respect to the lift is

15.

A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by

How long would the particle travel before coming to rest?

• 24m

• 40m

• 56m

• 56m

C.

56m

Velocity is rate of change of distance or displacement.
Distance travelled by the particle is

We know that, velocity is rate of change of distance i.e.,

but final velocity v = 0

Hence, distance travelled by the particle before coming to rest is given by

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16.

" Parsec " is the  unit of

• time

• distance

• frequency

• angular acceleration

A.

time

Parasec (pc) is an astronomical unit of length equal to the distance at which baseline of one astronomical unit subtends at an angle of one sec of arc.

1 parsec = 3.085677  × 1016 m = 3.26 light years

17.

Using mass (M), length (L), time (T) and current (A) as fundamental quantities, the dimension of permittivity is

• [ M L-2 T2 A ]

• [ M-1 L-3 T4 A2 ]

• [ M L T-2 A ]

• [ M L2 T-1 A2 ]

B.

[ M-1 L-3 T4 A2 ]

Force of attraction between two charges is given by

F =

=

( where 4$\mathrm{\pi }$ is dimensionless )

F = [ M-1 L-3 T4 A2 ]

18.

A body of mass 3 kg is under a constant force which causes a displacement s in metres in it, given by the relation , where t is in s. Work done by the force in 2 s is:

C.

If a constant force is applied on the object causing a displacement in it, then it is said that work has been done on the body to displace it.
Work done by the force  = Force x Displacement
or          W = F x s                            ...(i)
But from Newton's 2nd law, we have
Force  =  Mass x Acceleration
i.e.,       F = ma                                ...(ii)
Hence, from Eqs. (i) and (ii), we get

Hence, Eq (ii) becomes

We have given

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19.

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

• 150 m/s

• 27 m/s

• 450 m/s

• 250 m/s

A.

150 m/s

The relative velocity cf thief's jeep with respect to the police jeep

= 153 - 45 = 108 km/h

= 30 m/s

Therefore, striking speed = relative speed of bullet with respect to the thief's car

= 180 - 30 = 150 m/s

20.

When a ball is thrown up vertically with velocity  vo, it reaches a maximum height of h. If one wishes triple the maximum height then the ball should be thrown with velocity

• $\sqrt{3}$ vo

• 3vo

• 9vo

• 3/2 vo

A.

$\sqrt{3}$ vo

According to the Kinematic equation

v2 = u2 + 2 $\mathrm{\alpha }$s

∴   u2 ∝ s  or   ∝ s      ( since  u = vo )     ....(i)

For given condition

u'2 ∝ 3 s                                      .....(ii)

From eqn. (i) and (ii)

⇒   u' = $\sqrt{3}$vo