Circular Motion MSQ - Physics MCQ

Tangential acceleration is a_t = g cos θ which decrease with time.

Hence the plot of a_t versus time may be as shown in graph.

Area under graph in time interval t₁ = v_B – 0 = v_B

Area under graph in the time interval t₂ = v_C – v_B = v_B

Hence the under graph in time t₁ and t₂ is same.

∴  t₁ < t₂

∴ t₁ < t₂

The correct answers are: 

Let N be the normal reaction (Reading of the weighing machine)

Put v ∴  NA – mg = mg
⇒  N_A = 2mg = 2W

hence  N_A > N_E by 2W
Now at G, N_G = mg = W = N_c

The correct answers are: the weight reading at A is greater than the weight reading at E by 2 w, the weight reading at G = w, the ratio of the weight reading at E to that at A = 0, the ratio of the weight reading at A to that at C = 2

When he applies brakes

if µ is the friction coefficient then a = µg

when he takes turn 

 

Then we can see r < s₁ hence driver can hit the wall when he take turn due to insufficient radius of curvature.

The correct answer is: apply the brakes

As when they collide 

Now angle covered by 

Put t ∴ angle covered by 

The correct answers are: the time lapse for the two bodies to collide is  the angle covered of A is 11π/6

but R = K_x
(K = 1.47 × 10² N/m)
Also  r = 0.1 tan θ
put T, r, m  and ω in equation (2)
We have cos θ = 3/5 and T = 9.8 N
The correct answers are: Tension in spring is 9.8 N, Inclination of string with vertical is cos^–1(3/5)

The correct answers are: 0.5 sec, if    A can not catch B within 0.5 sec  

By putting the value of V_B

T_B = 3mg cosθ

When total acceleration vector directed horizontally

The correct answers are: total acceleration of sphere as a function of  thread tension as a function of θ is T = 3mg cos θ between the thread and the vertical at the moment when the total acceleration vector of the sphere is directed horizontal is 

By energy conservation between A and B

Now, radius of curvature 

The correct answers are: velocity at point B is   Radius of curvature of trajectory when leaves point B is R/2

Thus when h increases T also increases.
The correct answers are: increases as h increases, increases as α  increases