1

Which of the following is a fundamental unit?

A

Newton

B

Watt

C

Joule

D

Second

CORRECT OPTION:
d

2

A car moving with a speed of 90kmh^{-1} was brought uniformly to rest by the application of the brakes in 10s. How far did the car travel after the brakes were applied?

A

125m

B

150m

C

250m

D

15km

CORRECT OPTION:
c

speed = \(\frac{9 \times 10^3}{3600}\) = 25ms^{-1}

distance = speed x time

= 25 x 10 = 250m

distance = speed x time

= 25 x 10 = 250m

3

A particle of mass M which is at rest splits up into two. If the mass and velocity of one of the particles are m and v respectively, calculate the velocity of the second particle

A

\(\frac{mv}{M}\)

B

\(\frac{Mv}{M - m}\)

C

\(\frac{mv}{M + m}\)

D

\(\frac{mv}{M - m}\)

CORRECT OPTION:
d

(M - m)V_{2} = mv

V_{2} = \(\frac{mv}{M - m}\)

V

4

Which of the following statements are correct about an object in equilibrium under parallel forces? i. the total clockwise moments of the forces about any point equals the total anti-clockwise moments about the same point. ii. the total forces in one direction equals the total forces in the opposite direction. iii. the resolved components along the x-axis equals the resolved components along the y-axis.

A

i and ii only

B

i and iii only

C

ii and iii

D

i, ii, and iii only

CORRECT OPTION:
a

5

To keep a vehicle moving at a constant speed v, requires power P, from the engine. The force provided by the engine is

A

\(\frac{p}{v}\)

B

\(\frac{1}{2}\) v

C

pv

D

\(\frac{p}{v^2}\) v

CORRECT OPTION:
a

power = speed x force

force = \(\frac{power}{speed}\)

force = \(\frac{power}{speed}\)

6

A stone of mass m kg is held h meters above the floor for 50s. The work done in joules over this period is

A

mh

B

mgh

C

\(\frac{mgh}{50}\)

D

O

CORRECT OPTION:
d

work = mgh(no motion)

7

A body of mass 10kg rests on a rough inclined plane whose angle of tilt \(\theta\) is variable. \(\theta\) is gradually increased until the body starts to slide down the plane at 30^{o}. The coefficient of limiting friction between the body and the plane

A

0.30

B

0.50

C

0.58

D

0.87

CORRECT OPTION:
c

n = tan 30 = 0.58

8

An inclined plane which makes an angle of 30^{o} with the horizontal has a velocity ratio of

A

2

B

1

C

0.866

D

0.50

CORRECT OPTION:
a

V.R = \(\frac{1}{sin\theta}\)

= \(\frac{1}{sin30}\)

= 2

= \(\frac{1}{sin30}\)

= 2

9

What is the length of liquid column in a barometer tube that would support an atmospheric pressure of 102000Nm^{-2} if the density of the liquid is 2600kgm^{-3}? [g = 10ms^{-2}]

A

0.75m

B

0.76m

C

3.92m

D

39.23m

CORRECT OPTION:
c

pressure = g x density x height

102000 = 10 x 2600 x height

height = 3.92m

102000 = 10 x 2600 x height

height = 3.92m

10

40m^{3} of liquid is mixed with 60m^{3} of another liquid Q. If the density of P and Q are 1.00kgm^{-3} and 1.6kgm^{-3} respectively, what is the density of the mixture?

A

0.05kgm^{-3}

B

1.25kgm^{-3}

C

1.30kgm^{-3}

D

1.36kgm^{-3}

CORRECT OPTION:
d

M_{p} = 1 x 40 = 40kg ; mQ = 1.6 x 60 = 96kg

volume of mixture = 40 + 60 = 100m^{3}

mass of mixture = 40 + 96 = 136kg

density of mixture = \(\frac{136}{100}\)

= 1.36kgm^{3}

volume of mixture = 40 + 60 = 100m

mass of mixture = 40 + 96 = 136kg

density of mixture = \(\frac{136}{100}\)

= 1.36kgm

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