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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

172.

A car covers 2/5 of a certain distance with speed v₁ and rest 3/5 part with velocity v₂_. The average speed of the car is :

$\frac{1}{2} \sqrt{v_{1} v_{2}}$
$\frac{5 v_{1} v_{2}}{3 v_{1} + 2 v_{2}}$
$\frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$
$\frac{v_{1} + v_{2}}{2}$

173.
Apparent frequency of sound of engine is changing in the ratio 5/3 under the condition that engine is first aprroaching and then receding away from the observer. If velocity of sound is 340 m/s, then velocity of engine is

340 m/s

170 m/s

85 m/s

310 m/s

85 m/s

When source is moving towards stationary observer, its apparent frequency

$η_{1} = η (\frac{ν}{ν - v_{s}})$

where, ν $\to$ velocity of sound

ν_s $\to$ velocity of source

When source is moving away from observer, its apparent frequency

$η_{2} = η (\frac{ν}{ν + v_{s}})$

$∴$ $\frac{η_{1}}{η_{2}} = (\frac{ν}{ν - ν_{s}}) \times (\frac{ν + ν_{s}}{v})$

$\frac{5}{3} = \frac{ν + ν_{s}}{ν - ν_{s}}$

By solving,

$ν_{s} = \frac{ν}{4} = \frac{340}{4}$

= 85 m/s

174.

If a body travels half the distance with velocity v₁ and the next half with velocity v₂,its average velocity will be given by

$v = \sqrt{v_{1} v_{2}}$
$v = \frac{v_{1} + v_{1}}{2}$
$v = \frac{v_{1}}{v_{2}}$
$\frac{2}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$

175.

The ratio of the numerical value of the average velocity and average speed of body is always

unity
unity or less
unity or more
less than unity

176.

A wheel of car is revolving at the rate of 1200 cycle/min. On pressing the accelerator, after 10s, it does 4500 cycle/min then radial acceleration of the wheel is

30 rad/s²
1880 degree/s²
40 rad/s²
1980 degree/s²

177.

If a body loses half of its velocity on penetrating 3 cm in a wooden block then how much will it penetrate more before coming to rest?

1 cm
2 cm
3 cm
4 cm

178.

A stone is dropped in 19.6 m depth well, echo is heard in 2.06 s, then velocity of sound is

315.2 m/s
320.5 m/s
326.7 m/s
332.4 m/s

179.

An observer is coming towards plane mirror with a speed of 6 m/s, then apparent velocity of his image is

6 m/s
4 m/s
12 m/s
3 m/s

180.

A man wants to slide down a rope. The breaking load for the rope is $\frac{2}{3}$ rd ofthe weight of the man. With what minimum acceleration should fireman slide down?