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Two blocks of masses 2 kg and 5 kg are connected by an ideal string passing over a pulley. The block of mass 2 kg is free to slide on a surface inclined at an angle of 30° with the horizontal whereas 5 kg block hangs freely. The tension (T) in the string is

48.56 N
72.22 N
32.56 N
24.65 N

232.

A car is speeding on a horizontal road curving round with a radius of 60 m. The coefficient of friction between the wheels and the road is 0.5. The height of centre of gravity of the car from the road level is 0.3 m and the distance between the wheels is 0.8 m. Will the vehicle skid or topple ?

Yes, it will skid
No, it will not skid
Sometimes skid, sometimes not
Data insufficient to calculate speed for toppling

233.
A body starts rolling down on an inclined plane, the top half of which is perfectly smooth and lower half is rough. The angle of the plane being 30°, if the body is brought to rest just when it reaches the bottom, then the ratio of force of friction and weight of the body is

1 : 1

1 : 2

2 : 1

3 : 2

1 : 1

AB is an inclined plane of length 2l (for convenience) with centre C

$∠ ABO = θ = 30 °$

The top half AC of the plane is smooth and the lower half CB is rough. Let F be the force of friction in this part.

For the top half of inclined plane,

$u = 0, a = g \sin 30 ° = \frac{g}{2}, s = l, v = ? As v^{2} - u^{2} = 2 as ∴ v^{2} - 0 = 2 (\frac{g}{2}) l v = \sqrt{gl} For the bottom half of inclined plane, u = \sqrt{gl}, v = 0, s = l, a = ? As v^{2} - u^{2} = 2 as ∴ 0 - gl = 2 al a = \frac{- g}{2}$

$In this part, acceleration, a = \frac{net force}{mass} a = \frac{mg \sin 30 ° - F}{m} \frac{- g}{2} = g \times \frac{1}{2} - \frac{F}{m} or \frac{F}{m} = \frac{g}{2} + \frac{g}{2} = g or F = mg ∴ \frac{F}{mg} = \frac{1}{1}$

234.

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle θ should be

0°
30°
45°
60°

235.

Figure shows two blocks A and B pushed against the smooth wall with the force F. The wall is smooth but the surfaces in contact of A and B arerough. Which of the following is true for the system of blocks ?

The system can not be in equilibrium
F should be equal to weight of A and B
F should be less than theweight of A and B
F should be more than the weight of A and B

236.

A small block is shot into each of the four tracks as shown below. Each of the frictionless track rises to the same height. The speed, with which the block enters the tracks, is same in all cases. At the highest point of the track; normal reaction is maximum in

237.

A particle is placed at the origin and a force F = kx is acting on it (where k is positive constant). If u (O) = 0, the graph of u(x) versus x will be (where u is potential energy function)