Circular Motion NAT Level - 2

# Circular Motion NAT Level - 2

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## 10 Questions MCQ Test Topic wise Tests for IIT JAM Physics | Circular Motion NAT Level - 2

Circular Motion NAT Level - 2 for Physics 2022 is part of Topic wise Tests for IIT JAM Physics preparation. The Circular Motion NAT Level - 2 questions and answers have been prepared according to the Physics exam syllabus.The Circular Motion NAT Level - 2 MCQs are made for Physics 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Circular Motion NAT Level - 2 below.
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*Answer can only contain numeric values
Circular Motion NAT Level - 2 - Question 1

### A ball is projected making and angle θ with the vertical. Consider a small part of the trajectory near the highest position and take it approximately to be a circular arc. What is the radius of this circle? This radius is called the radius of curvature (ROC) of the curve at the point if u = 20 then ROC  in m.

Detailed Solution for Circular Motion NAT Level - 2 - Question 1

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Circular Motion NAT Level - 2 - Question 2

### A small wedge whose base is horizontal is fixed to a vertical rod as shown in the figure The slopping side of the wedge is frictionless and the wedge is spun with a constant angular speed ω about vertical axis as shown in the figure. Find The value of angular speed ω (rad/sec) for which the block of mass m just does not slide down the wedge?

Detailed Solution for Circular Motion NAT Level - 2 - Question 2

The free body diagram of the block is

For block not to slide along wedge, applying Newton's second law along incline we get

*Answer can only contain numeric values
Circular Motion NAT Level - 2 - Question 3

### The member OA rotates about a horizontal axis through O with a constant counter clockwise velocity  ω = 3 rad/sec. As it passes the position θ = 0, a small mass m is placed upon it at a radial distance r = 0.5m. If the mass is observed to slip at  θ = 37°, the coefficient of friction between the mass and the member is ____ .

Detailed Solution for Circular Motion NAT Level - 2 - Question 3

As the mass is at the verge of slipping

6 – 8µ = 4.5

*Answer can only contain numeric values
Circular Motion NAT Level - 2 - Question 4

A rod AB is moving on a fixed circle of radius R with constant velocity v’ as shown in figure. P is the point of intersection of the rod and the circle. At an instant the rod is at a distance x = 3R/5 from centre of the circle. The velocity of the rod is perpendicular to the rod and the rod is always parallel to the diameter CD.

The speed of point of intersection P is  then x is

Detailed Solution for Circular Motion NAT Level - 2 - Question 4

As a rod AB moves, the point ‘P will always lie on the circle.

x = 5

*Answer can only contain numeric values
Circular Motion NAT Level - 2 - Question 5

A squirrel climbing up a cylindrical post spirally makes the circle in a vertical height of four feet. If the top of the post is sixteen feet high and three feet in circumference, the distance travelled by it to reach the top is x in feet. Find the value of x/10

Detailed Solution for Circular Motion NAT Level - 2 - Question 5

Distance traveled in climbing 4 feet is
So, distance traveled in climbing 16 feet will be 20 feet x = 20 feet

x/10 = 2

*Answer can only contain numeric values
Circular Motion NAT Level - 2 - Question 6

The figure shows the velocity and acceleration of a point like body at the initial moment of its motion. The acceleration vector of the body remains constant. The minimum radius of curvature of trajectory of the body is (in m.)

Detailed Solution for Circular Motion NAT Level - 2 - Question 6

The acceleration vector shall change the component of velocity u|| along the acceleration vector.

Radius of curvature rmin means v is minimum and an is maximum. This is at point P when component of velocity parallel to acceleration vector becomes zero, that is u|| = 0.

*Answer can only contain numeric values
Circular Motion NAT Level - 2 - Question 7

A ring of mass 2π kg and of radius 0.25m is making 300 -rpm about an axis through its centre perpendicular to its plane. The tension (in newtons) developed in the ring is :

Detailed Solution for Circular Motion NAT Level - 2 - Question 7

*Answer can only contain numeric values
Circular Motion NAT Level - 2 - Question 8

A toy car of mass m can travel at a fixed speed. It moves in a circle on a fixed horizontal table. A string is connected to car and attached to a block of mass M = 5m that hangs as shown in figure (the portion of string below the table is always vertical). The coefficient of friction between the surface of table and tyres of the toy car is µ = 1. The ratio of the maximum radius to the minimum radius for which the toy car can move in a circular path with centre O on table is x/4, then x is:

Detailed Solution for Circular Motion NAT Level - 2 - Question 8

As the car travels at a fixed speed 1 m/s, hence tangential acceleration will be zero. Therefore, there will be no component of friction along tangent.

Case I : If  hence friction force on car of mass m will be outwards from the centre.

hence friction force on the car of mass m will be towards centre.

From equations (1) and (2)

*Answer can only contain numeric values
Circular Motion NAT Level - 2 - Question 9

A small bead of mass m = 1 kg is carried by a circular hoop having centre at C and radius r = 1m  which rotates about a fixed vertical axis (as shown). The coefficient of friction between bead and hoop is µ = 0.5. The maximum angular speed of the hoop for which the bead does not have relative motion with respect to hoop is given by (n√2)1/2.

Detailed Solution for Circular Motion NAT Level - 2 - Question 9

The maximum angular speed of the hoop corresponds to the situation when the bead is just about to slide upwards.
The free body diagram of the beads is

For the bead not to slide upwards

From 1 and 2 we get,

*Answer can only contain numeric values
Circular Motion NAT Level - 2 - Question 10

A circular curve of a highway is designed for traffic moving at 72 km/h. If the radius of the curved path is 100m, the correct angle of banking of the road should be given by :n tan-1(n).  Find the value of nAnswer

Detailed Solution for Circular Motion NAT Level - 2 - Question 10

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