Laws of Motion

• Question 573

Three concurrent co-planar forces 1 N, 2 N and 3 N acting along different directions on a bodycan keep the body in equilibrium if 2 N and 3 N act at right angle can keep the body in equilibrium if 1 N and 2 N act at right angle cannot keep the body in equilibrium can keep the body in equilibrium in 1 N and 3 N act at an acute angle

Solution

C.

cannot keep the body in equilibrium

If we keep 1 N and 2 N forces act in the same direction then these are balanced by 3 N force, but this is against statement of question.

Hence, options (c) is correct.

Question 574

Two rectangular blocks A and B of masses 2 kg and 3 kg respectively are connected by a spring of constant 10.8 Nm-1 and are placed on a frictionless horizontal surface. The block A was given an initial velocity of 0.15 ms-1 in the direction shown in the figure. The maximum compression of the spring during the motion is0.01 m 0.02 m 0.05 m 0.03 m

Solution

C.

0.05 m

As the block A moves with velocity 0.15 ms-1  it compresses the spring which pushes B towards right. A goes on compressing the spring till the velocity acquired by B becomes equal to the velocity of A, i.e., 0.15 ms-1.Let this velocity be v.

Now, spring is in a state of maximum compression. Let x be the maximum compression at this stage.

According to the law of conservation of linear momentum, we get

⇒               v =

⇒                   =

v = 0.06 ms-1

According to the law of conservation of energy

0.0225 - 0.009 =

0.0135 =

⇒                              x = $\sqrt{\frac{0.027}{\mathrm{k}}}$

⇒                                 = $\sqrt{\frac{0.027}{10.8}}$

x = 0.05 m

Question 575

A boy on a cycle pedals around a circle of 20 metres radius at a speed of 20 m/s. The combined mass of the body and the cycle makes with the vertical so that it may not fall is (g = 9.8 m/s2 )60.25o 63.90o 26.12o 30.00o

Solution

B.

63.90o

A body that travels an equal distance in equal amounts of time along a circular path has a constant speed but not constant velocity. This is because velocity is a vector and thus it has magnitude as well as direction.

v = ( Rg tanθ )1/2

=

tan θ = 63.70o

tanθ ≈ 63.90o

Question 576

A car of mass 1000 kg moves on a circular track of radius 40 m. If the coefficient of friction is 1.28. The maximum velocity with which the car can be moved, is22.4 m/s 112 m/s m/s 1000 m/s

Solution

A.

22.4 m/s

A car moves in a circular track so it perform circular motion.

According to second law the force providing this acceleration is

fc$\frac{{\mathrm{mv}}^{2}}{\mathrm{R}}$

But according to static friction

fs ≤ μs N

f =

Given:-  μ = 1.28

where μ is  the coefficient of friction

R = 40 m

The maximum velocity

vmax

=

vmax = 22.4 m/s