A heavy block of mass m is slowly placed on a conveyer belt moving with speed v. If coefficient of friction between block and the belt is μ, the block will slide on the belt through distance

A direct rope haulage pulls 8 tubs loaded with coal through an incline of length 500 m having an inclination of 1 in 6. Consider the following additional data.
Capacity of tub = 1.0 tonne.
Tare weight of tub = 500 kg
Hauling speed = 9 km per hour
Coefficient of friction between wheel and rail = $$\frac{1}{{60}}$$
Coefficient of friction between rope and drum = $$\frac{1}{{10}}$$
Mass of rope per meter = 1.5 kg
The minimum power required to haul the tubs in kW is

A

345.50

B

348.60

C

350.10

D

365.50

E

58.86

The ratio of belt tensions $$\frac{{{{\text{p}}_1}}}{{{{\text{p}}_2}}}$$ considering centrifugal force in flat belt is given by where,
m = mass of belt per meter (kg/m)
v = belt velocity (m/s)
f = coefficient of friction
$$\alpha $$ = angle of wrap (radians)

A

$$\frac{{{{\text{p}}_1} - {\text{m}}{{\text{v}}^2}}}{{{{\text{p}}_2} - {\text{m}}{{\text{v}}^2}}} = {{\text{e}}^{{\text{f}}\alpha }}$$

B

$$\frac{{{{\text{p}}_1}}}{{{{\text{p}}_2}}} = {{\text{e}}^{{\text{f}}\alpha }}$$

C

$$\frac{{{{\text{p}}_1}}}{{{{\text{p}}_2}}} = {{\text{e}}^{ - {\text{f}}\alpha }}$$

D

$$\frac{{{{\text{p}}_1} - {\text{m}}{{\text{v}}^2}}}{{{{\text{p}}_2} - {\text{m}}{{\text{v}}^2}}} = {{\text{e}}^{ - {\text{f}}\alpha }}$$

A block of mass 1kg is given a velocity of 5m/s on a horizontal flat surface. What will be the change in internal energy of the block-surface system, when the block comes to rest. The coefficient of kinetic friction is 0.3 and coefficient of static friction is 0.4.

A

25J

B

12.5J

C

0

D

30J

What is the monoisotopic and average mass of valine? Given data: Mass of the most abundant isotope of Carbon (C°)=12.0000, Mass of most abundant isotope of Hydrogen (H°)=1.0078, Mass of most abundant isotope of Oxygen (O°)=15.9949, Mass of most abundant isotope of Nitrogen (N°)=14.0031, The average mass of Carbon (C)=12.011, The average mass of Hydrogen (H)=1.008, The average mass of Oxygen (O)=15.999, The average mass of Nitrogen (N)=14.007.

A

99.068 and 99.2361

B

99.216 and 99.326

C

99.111 and 99.321

D

99.068 and 99.132

A spring block system is on a horizontal surface. The block is compressed by 10cm. What should be the coefficient of friction between the block and ground such that the block comes to a stop at the mean position? Mass of block = 0.5kg & spring constant = 3N/m.

A

0.03

B

0.06

C

0.12

D

0.05

A mass of 4kg rests on a horizontal plane. The plane is gradually inclined until at an angle θ= 15° with the horizontal, the mass just begins to slide. What is the coefficient of static friction between the block and the surface?

A

0.814

B

0.27

C

1.5

D

3.5

A wooden block is kept on a polished wooden plank and the inclination of the plank is gradually increased. It is found that the block starts slipping when the plank makes an angle of 18° with the horizontal. However, once started the block can continue with uniform speed if the inclination is reduced to 15°. Find the coefficient of static friction between the block and the plank.

A

tan 180

B

tan 150

C

tan 330

D

tan 30

A wooden block is kept on a polished wooden plank and the inclination of the plank is gradually increased. It is found that the block starts slipping when the plank makes an angle of 18° with the horizontal. However, once started the block can continue with uniform speed if the inclination is reduced to 15°. Find the coefficient of kinetic friction between the block and the plank.

A

tan 180

B

tan 150

C

tan 330

D

tan 30

Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the three statements and give answer. There are six letters E, I, P, G, N and O is PIGEON the word formed after performing the following operations using these six letters only? I. O is placed fourth to the right of P. G is not placed immediately next to either P or O. II. N is placed immediately next (either left or right) to O. E is placed immediately next (either left or right) to G. III. Both I and E are placed immediately next to G. The word does not begin with N. P is not placed immediately next to E.

A

If the data in statement I and II are sufficient to answer the question, while the data in statement III alone are not sufficient to answer the question.

B

If the data in statement I and III are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

C

If the data in statement II and III are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

D

If the data either statement I alone or statement II alone or statement III alone are sufficient to answer the question.

We have two types of a coefficient of friction, one is coefficient of static friction and the other one is the coefficient of the kinetic friction.

A

True

B

False