**1. A body is resting on a plane inclined at angle of 30° to horizontal. What force would be required to slide it down, if the coefficient of friction between body and plane is 0.3?**

(a) 5 kg

(b) 1 kg

(c) zero

(d) 0.5 kg

Answer

Option (c) is correct

**Force will be required to slide it down if**

\(\mu mg \cos \theta>mg\sin \theta\)

\(0.3\times mg \times \frac{\sqrt 3}{2}>mg\times\frac{1}{2}\)

\(mg \times \frac{0.519}{2}>mg\times\frac{1}{2}\)

**So we see that above relation is not true hence no force** **required to slide it down, as it will automatically slide due to its own weight.**

**2. Compression members tend to buckle in the direction of **

(a) least radius of gyration

(b) axis of load

(c) perpendicular to axis of load

(d) minimum cross–section

Answer

Option (a) is correct

**Compression members tend to buckle in the direction of least radius of gyration.**

**3. A fluid jet discharging from 150 mm diameter orifice has a diameter of 100 mm at its vena contracta. The coefficient of contraction is**

(a) 0.44

(b) 1.24

(c) 0.24

(d) 0.64

Answer

Option (a) is correct

**The coefficient of contraction is given as**

\(\large C_c=\frac{a_c}{a}=\frac{\pi/4 (100)^2}{\pi/4 (150)^2}=\frac{4}{9}=0.44\)

**4. The escape velocity on the surface of the earth is **

(a) 11.2 km/sec

(b) 1 km*/*sec

(c) 3.6 km*/*sec

(d) 8.8 km/sec

Answer

Option (a) is correct

**Escape velocity is defined to be the minimum velocity an object must have in order to escape the gravitational field of the earth, that is, escape the earth without ever falling back. It is 11.2 km/sec.**

**5. The heat to be supplied to a Carnot engine operating between 800 and 400 K and producing 100 kJ of work, is **

(a) 100 kJ

(b) 200 kJ

(c) 300 kJ

(d) 400 kJ

Answer

Option (b) is correct

**Efficiency is given as**

\(\large \eta=1-\frac{400}{800}=0.5\)

\(\large \eta=0.5=\frac{100}{Q_1}\)

\(Q_1=200\;kJ\)

**6. A piece of wood having weight of 10 kg floats in water with 60% of its volume under the liquid. Determine the specific Gravity of wood. **

(a) 0.6

(b) 0.83

(c) 0.4

(d) 0.3

Answer

Option (a) is correct

**Balancing the forces, we have**

\((0.6V)\rho_wg=V\rho_og\)

\(\large \frac{\rho_o}{\rho_w}=0.6\)

**7. If all the dimension of a prismatic bar be increased in the ratio of k:1, then maximum stress produced in the bar due to its own weight will increase in the following ratio**

(a) 1 : k

(b) k^{2} : 1

(c) k^{3} : 1

(d) k : 1

Answer

Option (d) is correct

**Let the force unit volume be given as**

\(\large \rho=\frac{F}{lbh}\)

**Case I**

**Max stress is given as**

\(\large \sigma_1=\frac{\rho g\times lbh}{bh}=\rho gl\)

**Case II**

**Max stress is given as**

\(\large \sigma_2=\frac{\rho g\times klkbkh}{kbkh}=\rho gkl\)

**Taking the ratio, we get**

\(\large \frac{\sigma_2}{\sigma_1}=k\)

\(\sigma_2:\sigma_1=k:1\)

**8. A house requires 60M cal/hr in winter for heating. Heat pump absorbs heat from cold air outside and requires 8M cal/hr of work. The COP will ****be**

(a) 0*.**75 *

(b) 7.5

(c) 6.5

(d) 10

Answer

Option (b) is correct

**COP is given as**

\(\large COP=\frac{Q_2}{W}=\frac{60}{8}=7.5\)

**9. A body moves, from rest with a constant acceleration of 5 m per sec**^{2}. The distance covered in 10 sec is most nearly

(a) 200 m

(b) 300 m

(c) 250 m

(d) 500 m

Answer

Option (c) is correct

**Using equation of motion, we have**

\(s=ut+0.5at^2=0+0.5\times5\times100=250\;m\)

**10. A cold storage plant of 20 tonne of refrigerator capacity operates between 200 and 300 k. The power required to run the plant if the plant has half COP of a Carnot cycle (Tonne of refrigerator = 3.5 kW) is **

(a) 50 kW

(b) 60 kW

(c) 70 kW

(d) 80 kW

Answer

Option (c) is correct

**COP of Carnot refrigerator is given as**

\(\large COP_c=\frac{200}{300-200}=2\)

**COP of actual refrigerator**

\(\large COP=\frac{COP_c}{2}=1\)

\(\large COP=1=\frac{3.5\times20}{W}\)

\(W=70\;kW\)

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