Three blocks of masses m₁, m₂ and m3 are connected by mass less strings, as shown, on a friction less table. They are pulled with a force T₃ = 40 N. If m₁ = 10 kg, m₂= 6 kg and m₃ = 4kg, the tension T₂ will be

20 N
40 N
10 N
32 N

Solution

The linear momentum p of a body moving in one dimension varies with time according to the equating P = a + bt² where a and b are positive constants. The net force acting on the body is

proportional to t²
a constant
proportional to t
inversely proportional to t

Solution

Linear momentum, P = a + bt²

^dp⁄_dt = 2bt(on differentiation)

∴ Rate of change of momentum, ^dp⁄_dt ∝ t

By 2nd law of motion, ^dp⁄_dt ∝ F

∴ F ∝ t

Two pulley arrangements of figure given are identical. The mass of the rope is negligible. In fig (a), the mass m is lifted by attaching a mass 2m to the other end of the rope. In fig(b), m is lifted up by pulling the other end of the rope with a constant downward force F =2mg. The acceleration of m in the two cases are respectively

3g, g
g/3, g
g/3, 2g
g, g/3

Solution

Let a and a' be the accelerations in both cases respectively. Then for fig (a),

T – mg = ma … (1)

and 2mg – T = 2ma … (2)

Adding (1) and (2), we get

mg = 3ma

∴ a = ^g⁄₃

For fig (b),

T' - mg = ma' … (3)

and 2mg - T' = 0 … (4)

Solving (3) and (4)

a' = g

∴ a = ^g⁄₃ and a' = g

When the road is dry and the coefficient of the friction is μ,the maximum speed of a car in a circular path is 10 ms^-1. If the road becomes wet and μ’=^μ⁄₂, what is the maximum speed permitted?

5 ms^-1
10 ms^-1
10√2 ms^-1
5√2 ms^-1

Solution

v_max=\(\sqrt{\mu gr}\)

A person with his hand in his pocket is skating on ice at the rate of 10m/s and describes a circle of radius 50 m. What is his inclination to vertical :(g = 10 m/sec²)

tan^-1(½)
tan^-1(1/5)
tan^-1(3/5)
tan^-1(1/10)

Solution

Since surface (ice) is friction less, so the centripetal force required for skating will be provided by inclination of boy with the vertical and that angle is given as

tan θ=^v²⁄_rg where v is speed of skating & r is radius of circle in which he moves.

A small sphere is attached to a cord and rotates in a vertical circle about a point O. If the average speed of the sphere is increased, the cord is most likely to break at the orientation when them ass is at

bottom point B
the point C
the point D
top point A

Solution

A circular road of radius r in which maximum velocity is v,has angle of banking

tan^-1(^v²⁄_rg)
tan^-1(^rg⁄_v²)
tan^-1(^v⁄_rg)
tan^-1(^rg⁄_v)

Solution

From figure,

N sin θ=^mv²⁄_r....... (i)

N cos θ= mg...... (ii)

Dividing, we get

tan θ=^v²⁄_rg or θ=tan^-1(^v²⁄_rg)

A cane filled with water is revolved in a vertical circle of radius 4 meter and the water just does not fall down. The time period of revolution will be

1 sec
10 sec
8 sec
4 sec

Solution

A bucket tied at the end of a 1.6 m long string is whirled in a vertical circle with constant speed. What should be the minimum speed so that the water from the bucket does not spill when the bucket is at the highest position?

4 m/sec
6.25 m/sec
6.25 m/sec
None of the above

Solution

The coefficient of friction between the rubber tyres and the road way is 0.25. The maximum speed with which a car can be driven round a curve of radius 20 m without skidding is(g = 9.8 m/s²)

5m/s
7 m/s
10 m/s
14 m/s

Solution

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