Basic Science Test 20

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Basic Science Test 20

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Question 1
1 / -0

If $$a_1 $$ and $$a_2$$ are two non collinear unit vector unit and if $$|a_1 +a_2| =\sqrt 3$$, then the value of $$(a_1-a_2), (2a_1 +a_2)$$ is

A
$$2$$

B
$$\dfrac 32$$

C
$$\dfrac 12$$

D
$$113$$ There are $$N$$ coplaner vectors each of

Solution

$$|a_1 +a_2|=\sqrt 3$$
$$\Rightarrow \sqrt {1+2\cos \theta}=\sqrt 3$$
$$\Rightarrow 2+2 c \theta =3$$
$$\Rightarrow 2x \theta =1\Rightarrow c\theta =\dfrac 12$$
$$(a_1 -a_2).(2a_1 +a_2)$$
$$=2a_1^2 +a_1.a_2 -2a_1.a_2-a_2^2$$
$$(\because a_1^2 =a_2^2 =a_1 .a_1 =|a_1| (a_1) \cos \theta =1)$$
$$=2-1+\dfrac {1}{2}-\dfrac {2}{2}=\dfrac {1}{2}$$
Question 2
1 / -0

The velocity at the maximum height of a projectile is half of its initial velocity of projection. The angle of projection is

A
$$30^{\circ}$$

B
$$45^{\circ}$$

C
$$60^{\circ}$$

D
$$76^{\circ}$$

Solution

Let initially velocity is $$V$$
So, at the highest point only horizontal velocity exists i.e. $$V_{horizontal} = \dfrac{V}{2}$$
Now, $$V_{horizontal} = \dfrac{V}{2}= Vcos \theta$$
$$\implies \cos\theta = \dfrac{1}{2}$$
$$\implies \theta = 60^{\circ}$$
Question 3
1 / -0

The relation between the time of flight a projectile $$ T_{f} $$ and the time to reach the maximum height $$ t_{m} $$ is

A
$$ T_{f} 2t_{m} $$

B
$$ T_{f} = t_{m} $$

C
$$ T_{f} = \dfrac{t_{m}}{2} $$

D
$$ T_{f} = \sqrt{2}(t_{m}) $$

E
$$ T_{f} = \dfrac{t_{m}}{\sqrt{2}} $$
Question 4
1 / -0

The displacement x and time t for a particle are related to each other as $$ t = \sqrt{x} + 3 $$ . What is work done in first six seconds of its motion ?

A
6 J

B
zero

C
4 J

D
2 J
Question 5
1 / -0

An electric motor uses 2 amperes of current when connected to a 12 volt battery to raise a 20 newton object vertically at constant velocity . If the energy conversion was 100 % efficient , the object be raised at a speed of

A
0.6 m/s

B
1.2 m/s

C
6 m/s

D
24 m/s
Question 6
1 / -0

If the force applied is F and the velocity galance is v , then the average power developed is :-

A
$$\dfrac{F}{v}$$

B
$$\dfrac{v}{F}$$

C
$$\dfrac{Fv}{2}$$

D
$$ Fv^{2} $$
Question 7
1 / -0

Two object A and B are moving with velocities $$ v_{A} and v_{B} $$ respectively a,long positive x - axis If $$ v_{A} < v_{B} $$ which of the following position time graph correctly showing the velocity of A and B ?

A

B

C

D
Question 8
1 / -0

A uniform thin bar of mass length 12 L is bent to make a regular hexagonal . Its moment of lines about an axis passing through the centre of mass and perpendicular to the plane of the hexagonal is -

A
20 $$ mL^{2}$$

B
6 $$ mL^{2}$$

C
$$\dfrac{12}{5} mL^{2}$$

D
30 $$ mL^{2}$$
Question 9
1 / -0

If change in displacement is proportional to time in the class of 1 - dimensional motin

A
velocity is varible

B
velocity is constant is magnitude only

C
velocity is constant in direction only

D
velocity is constant
Question 10
1 / -0

Three blocks of mass 2 kg. 3 kg andd 5kg are concted to each other with light strings and are then placed on a smooth frictional surface. The system i pulled with a force F from the side of the lighter mas so that it moves with an acceleration lighter mass so that it moves with an acceleration of $$1 ms ^{-2}$$ T_{1}$$, nd $$T_{2}$$ denote the tensions in the other strings The value of F is :

A
$$2N$$

B
$$3N$$

C
$$5 N$$

D
$$10 N$$