1

At what respective values of X, Y and Z would the unit of force, the newton, be dimensionally equivalent to M^{x}L^{y}T^{z}?

A

-1, 1, 2

B

1, 1, -2

C

1, -1, 2

D

-1, 1, -2

CORRECT OPTION:
b

F = m (v-u)

= kg x m x S^{-2}

= M^{1}L^{1}T^{-2}

= kg x m x S

= M

2

The distance xm travelled by a particle in time t seconds is described by the equation x = 10 + 12t^{2}, Find the average speed of the particle between the time interval t = 2s and t = 5s

A

60 ms^{-1}

B

72 ms^{-1}

C

84 ms^{-1}

D

108 ms^{-1}

CORRECT OPTION:
b

speed = \(\frac{dx}{dt}\)

\(\frac{dx}{dt}\) = 10 + 12t^{2}

\(\frac{dx}{dt}\) = 24t

\(\frac{dx}{dt}\) =24 x 3

\(\frac{dx}{dt}\) = 72 ms^{-1}

\(\frac{dx}{dt}\) = 10 + 12t

\(\frac{dx}{dt}\) = 24t

\(\frac{dx}{dt}\) =24 x 3

\(\frac{dx}{dt}\) = 72 ms

3

A 5kg block is released from rest on a smooth plane inclined at an angle of 30^{o} to the horizontal. What is the acceleration down the plane? [g = 10ms^{-2}]

A

5.0 ms^{-2}

B

5.8 ms^{-2}

C

8.7 ms^{-2}

D

25.0 ms^{-2}

CORRECT OPTION:
a

ma = mgsin\(\theta\)

a = \(\frac{5 {\times} 10 {\times} sin30}{t}\)

a = 5ms^{2}

a = \(\frac{5 {\times} 10 {\times} sin30}{t}\)

a = 5ms

4

An arrow of mass 0.1kg moving with a horizontal velocity of 15ms^{-1} is shot into a wooden block of mass 0.4kg lying at rest on a smooth horizontal surface. Their common velocity after impact is

A

15.0 ms^{-1}

B

7.5 ms^{-1}

C

3.8 ms^{-1}

D

3.0 ms^{-1}

CORRECT OPTION:
d

M_{1}U_{1} + M_{2}U_{2}

= (m_{1} + m_{2})v

= \(\frac{(0.1 {\times} 15) + (0.4 {\times} 0)}{(0.1 + 0.4)}\)

v = 3ms^{-1}

= (m

= \(\frac{(0.1 {\times} 15) + (0.4 {\times} 0)}{(0.1 + 0.4)}\)

v = 3ms

5

Two bodies X and Y are projected on the same horizontal plane, with the same initial speed but at angles 30 and 60 respectively to the horizontal. Neglecting air resistance, the ratio of the range of X to that of Y is

A

1:1

B

1:2

C

√3:1

D

√3

CORRECT OPTION:
a

Range = \(\frac{U^2sin2{\theta}}{g}\)

\(\frac{R_x}{R_y}\) = \(\frac{U^2_xsin60}{U^2_ysin120}\)

sin60^{o} = sin120^{o}

\(\frac{R_x}{R_y}\) = \(\frac{1}{1}\)

hence, = 1:1

\(\frac{R_x}{R_y}\) = \(\frac{U^2_xsin60}{U^2_ysin120}\)

sin60

\(\frac{R_x}{R_y}\) = \(\frac{1}{1}\)

hence, = 1:1

6

Which of the following with respect to a body performing simple harmonic motion are in phase?

A

displacement and velocity of the body

B

displacement and force on the body

C

velocity and acceleration of the body

D

force acting on the body and the acceleration

CORRECT OPTION:
c

7

A body of mass 2kg moving vertically upwards has its velocity increased uniformly from 10ms^{-1} to 40ms^{-1} in 4s. Neglecting air resistance, calculate the upward vertical force acting on the body.[g = 10 ms^{-1}]

A

15N

B

20N

C

35N

D

45N

CORRECT OPTION:
c

F = mg + ma

F = 2 [10 + \(\frac{(40 - 10)}{4}\)]

F = 35 N

F = 2 [10 + \(\frac{(40 - 10)}{4}\)]

F = 35 N

8

A planet has mass m_{1} and is at a distance r, from the sun. A second planet has mass m_{2} = 10m_{1} and at a distance of r_{2} = 2r_{1} from the sun. Determine the ratio of the gravitational force experienced by the planets.

A

1 : 5

B

2 : 5

C

3 : 5

D

4 : 5

CORRECT OPTION:
b

g = \(\frac{GM}{R^2}\)

\(\frac{G_1M_1}{r^2_1}\) = \(\frac{G_2M_2}{r^2_2}\)

\(\frac{G_1M_1}{r^2_1}\) = \(\frac{G_2 {\times}10 M_1}{(2r_1)^2}\)

\(\frac{G_1}{G_2}\) = \(\frac{2}{5}\)

\(\frac{G_1M_1}{r^2_1}\) = \(\frac{G_2M_2}{r^2_2}\)

\(\frac{G_1M_1}{r^2_1}\) = \(\frac{G_2 {\times}10 M_1}{(2r_1)^2}\)

\(\frac{G_1}{G_2}\) = \(\frac{2}{5}\)

9

An object of mass 100g projected vertically upwards from the ground level has a velocity of 20ms^{-1} at a height of 10m. calculate its initial kinetic energy at the ground level.[g = 10ms^{-2}, neglect air resistance]

A

10 J

B

20 J

C

30 J

D

50 J

CORRECT OPTION:
c

Using, v^{2} = u^{2} - 2gx

(20)^{2} = u^{2}1/2 x 10 x 10

u^{2} = 600(m/s)^{2}

initial K.E = - mu^{2}

= \(\frac{1}{2}\) x 600

= 30 J

(20)

u

initial K.E = - mu

= \(\frac{1}{2}\) x 600

= 30 J

10

An electric water pump rate 1.5 kW, lifts 200kg of water through a vertical height of 6 meters in seconds. What is the efficiency of the pump? [g = 10ms^{-2}, neglecting air resistance]

A

90.0%

B

85.0%

C

80.0%

D

65.0%

CORRECT OPTION:
c

Efficiency = output x 100

= \(\frac{\frac{200 {\times} 10 {\times} {\theta}}{10}}{1500}\) x \(\frac{100}{1}\)

= 80%

= \(\frac{\frac{200 {\times} 10 {\times} {\theta}}{10}}{1500}\) x \(\frac{100}{1}\)

= 80%

Pages: