Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Physics 35 Years JEE Main & Advanced Past year Papers

JEE : Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

The document Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev is a part of the JEE Course Physics 35 Years JEE Main & Advanced Past year Papers.
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Q.1. A bullet is fired from a rifle. If the rifle recoils freely, determine whether the kinetic energy of the rifle is greater than, equal or less than that of the bullet. (1978)

Ans. Less than

Solution. Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Q.2. 

A spring of force constant k is cut into three equal parts.

What is force constant of each part?

Ans. 3 times

Solution. KEYCONCEPT : For a spring, (spring constant) × (length) = Constant If length is made one third, the spring constant becomes three times.

Q.3. A 20 gm bullet pierces through a plate of mass M1 = 1 kg and then comes to rest inside a second plate of mass M2 = 2.98 kg. as shown. It is found that the two plates initially at rest, now move with equal velocities. Find the percentage loss in the initial velocity of the bullet when it is between M1 and M2. Neglect any loss of material of the plates due to the action of the  bullet. (1979)

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Ans. 25%

Solution. Let v be the velocity of bullet before striking A. Applying conservation of linear momentum for the system of bullet and plate A, we get 0.02v = 0.02 v1 + 1 × v2

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Again applying conservation of linear momentum for collision at B. 

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

From (i) and (ii)

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Q.4. When a ball is thrown up, the magnitude of its momentum decreases and then increases. Does this violate the conservation of momentum principle?

Ans. No

Solution. No. An external force, the gravitational pull of earth, is acting on the ball which is responsible for the change in momentum.

Q.5. In the figures (a) and (b) AC, DG and GF are fixed inclined planes, BC = EF = x and AB = DE = y. A small block of mass M is released from the point A. It slides down AC and reaches C with a speed Vc. The same block is released from rest from the point D. It slides down DGF and reaches the point F with speed VF. The coefficients of kinetic frictions between the block and both the surface AC and DGF are m. (1980) Calculate VC and VF.

Ans. Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Solution. K.E. at C = Loss in P.E. – Work done by friction.

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

= gy -µgx

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

K.E. at F = loss in P.E. – Work done by friction

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Note : The result does not depend on the angles a and b. It only depends on the values of x and y.

Q.6. Two block s A an d B a re connected to each other by a string and a spring ; the string passes over a frictionless pulley as shown in the figure. Block B slides over the horizontal top  surface of a stationary block C and the block A slides along the vertical side of C, both with the same uniform speed.

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

The coefficient of friction between the surfaces of blocks is 0.2. Force constant of the spring is 1960 newtons/m. If mass of block A is  2 Kg., calculate the mass of block B and the energy stored in the spring. (1982 - 5 Marks)

Ans. 10 kg, 0.098 J

Solution. 

Since the two blocks A and B are moving with constant velocity, therefore, the net force acting on A is zero and the net force acting on B will be zero. Since the spring is loaded, it will be in a deformed state. Let the extension of the spring be x.

The forces are drawn.

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Note : There will be no friction force between block A and C ∴ f = µN. Her e t h ere is no normal reaction on A (because A is not pushing C)

 Applying Fnet = ma on A, we get

mAg – T = mA × 0

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

ApplyingSubjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

T – f = mB × 0

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

= µmBg ... (ii)

From (i) and (ii)

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Here the force acting on the spring is the tension (equal to restoring force)

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

The P.E. stored in spring is given by

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Q.7. A 0.5 kg block slides from the point A (see Fig)  on a horizontal track with an initial speed of 3 m/s towards a weightless horizontal spring of length 1 m and force constant  2 Newton/ m. The part AB of the  track  is frictionless and the part  BC has the coefficients of static and kinetic friction as 0.22 and 0 2 respectively. If the distances AB  and BD are 2 m and 2.14 m respectively, find the total distance  through which the block moves before it comes to rest completely. (Take g = 10m / s2) (1983 - 7  Marks)

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Ans. 4.24 m

Solution. K.E. of block = work against friction + P.E. of spring

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

On solving, we get x Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Here the body stops momentarily.

Restoring force at Y = kx = 2 × 0.1 = 0.2 N

Frictional force at Y = µs mg = 0.22 × 0.5 × 9.8 = 1.078 N

Since frictional force > restoring force, the body will stop here.

∴ The total distance travelled

= AB + BD + DY = 2 + 2.14 + 0.1 = 4.24 m.

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Q.8. A string, with one end fixed on a rigid wall, passing over a fixed frictionless pulley at a distance of 2m from the wall, has a point mass  M = 2kg attached to it at a distance of 1m from the wall. A mass m = 0.5 kg attached at the free end is held at rest so that the string is horizontal between the wall and the pulley and vertical beyond the pulley. What will be the speed with which the mass M will hit the wall when the mass m is released ? (1985 - 6 Marks)

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Ans. 3.29 m/s

Solution. 

When mass m is released, since M > m, the mass M will move on a dotted path with O as the centre. There will be decrease in the potential energy of M which will be converted into kinetic energy of M, and increase in potential energy of m.

Decrease in P.E. of M is Mgh 

= 2 × 9.8 × 1 = 19.6 J

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

(Let V be the velocity attained by M just before striking the wall)

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

From the figure, by velocity constraint 

v = V cos θ

From ΔOAC,

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

(OC + CA) – OA = height attained by m

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

NOTE THIS STEP

By the principle of energy conservation

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

On solving, we get  V = 3.29 m/s

Q.9. A simple pendulum is suspended from a peg on a vertical wall. The pendulum is pulled away from the wall to a horizontal position (see fig.) and released. The 2/√5 ball hits the wall, the coefficient of restitution being 

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

What is the minimum number of collisions after which the amplitude of oscillations becomes less than 60 degrees ?

Ans. 4

Solution. 

The pendulum bob is left from position A. When it is at position C, the angular amplitude is 60°.

In ΔOCM

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

The velocity of bob at B, vB before first collision is

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Let after n collisions, the angular amplitude is 60° when the bob again moves towards the wall from C, the velocity v'B before collision is

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

This means that the velocity of the bob should reduce from

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

The final velocity after n collisions is √gl

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

where e is coefficient of restitution.

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Taking log on both sides we get

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Therefore, number of collisions will be 4.

Q.10.  Two blocks of mass 2 kg and M are at rest on an inclined plane and are separated by a distance of 6.0 m as shown in Figure. The coefficient of friction between each of the blocks and the inclined plane is 0.25. The 2 kg block is given a velocity of 10.0 m/s up the inclined plane. It collides with M, comes back and has a velocity of 1.0 m/s when it reaches its initial position. The other block M after the collision moves 0.5 m up and comes to rest. Calculate the coefficient of restitution between the blocks and  the mass of the block M. [Take sin q » tan q = 0.05 and g = 10m / s 2 . ] (1999 - 10 Marks)

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Ans.  0.84; 15.02 kg.

Solution. Fr om A to B. 

u = 10 m/s    (given)

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

v = ?

s = 6 m

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

⇒ The velocity of mass m just before collision is 8 m/s.

The velocity of mass M just before collision is 0 m/s (given).

AFTER COLLISION

Let v1 be the velocity of mass m after collision and v2 be the velocity of mass M after collision. Body of mass M moving from B to C and coming to rest. 

u = v2

 v = 0

 a = – 2.99 m/s2

 (same as of previous case because all other things are same except mass. a is independent of mass) s = 0.5

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Body of mass m moving from B to A after collision

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

h = 6 sin θ = 6 × 0.05      

u = v1 

v = + 1m/s

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

v1 = – 5 m/s

Coefficient of restitution

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

On applying conservation of linear momentum before and after collision, we get 

2 × 8 + M × 0 = 2 × (– 5) + M (1.73)

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Q.11. A spherical ball of mass m is kept at the highest point in the space between two fixed, concentric spheres A and B (see figure). The smaller sphere A has a radius R and the space between the two spheres has a width d. The ball has a diameter very slightly less than d. All surfaces are frictionless. The ball is given a gentle push (towards the right in the figure). The angle made by the radius vector of the ball with the upward vertical is denoted by θ (shown in the figure). (2002 - 5 Marks)

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev


(a) Express the total normal reaction force exerted by the sphere on the ball as a function of angle θ.

 (b) Let NA and NB denote the magnitudes of the normal reaction forces on the ball exerted by the sphere A and B, respectively. Sketch the variations of NA and NB as functions of cos q in the range Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

 by drawing two separate graphs in your answer book, taking cos θ on the horizontal axes.

Ans.  (a)  NA = mg (3cosθ – 2)

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Solution. The ball is moving in a circular motion. The necessary centripetal force is provided by (mg cosθ – N). Therefore,

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

According to energy conservation

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

From (i) and (ii) 

NA = mg (3 cos θ – 2) ... (iii

The above equation shows that as q increases NA decreases.

At a particular value of q , NA will become zero and the ball will lose contact with sphere A. This condition can be found by putting NA = 0 in eq. (iii)

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

The graph between Nand cosθ From equation (iii) when q = 0, NA = mg.

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

The graph is a straight line as shown.

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Using energy conservation

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

From (iv) and (v), we get

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Subjective Type Questions: Work, Energy and Power | JEE Advanced Notes | EduRev

Therefore the graph is as shown.

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