JEE Main PYQs on Forces: JEE Main Questions for Practice with Solutions

1.

A force $ 6 \hat{k} $ is applied for $ \frac{5}{3} $ seconds on a body of mass 2 kg. If the initial velocity of the body was $ 3\hat{i} + 4\hat{j} $, then find the final velocity of the body.

• \( 3\hat{i} + \hat{j} + 5\hat{k} \)
• \( 3\hat{i} + 4\hat{j} + 5\hat{k} \)
• \( 3\hat{i} + 2\hat{j} - 3\hat{k} \)
• \( 3\hat{i} + 4\hat{j} - 5\hat{k} \)

2.

A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string passing over a frictionless pulley as shown below.
The coefficient of kinetic friction between the surface and block is 0.02. The acceleration of the block is (Given g = 10 ms^–2)

• 1 ms^–2
• \(\frac{1}{5}\) ms^–2

• \(\frac{4}{5}\) ms^–2

• \(\frac{8}{11}\) ms^–2

3.

Two forces \(F_1\) and \(F_2\) are applied on two rods \(P\) and \(Q\) of same materials such that elongation in rods are same. If ratio of their radii is \(x : y\) and ratio of length is \(m : n\), then ratio of \(F_1 : F_2\) is

• \(\bigg(\frac{y}{x}\bigg)^2\frac{ n}{m}\)
• \(\bigg(\frac{x}{y}\bigg)^2 \frac{n}{m}\)
• \(\bigg(\frac{y}{x}\bigg)^2 \frac{m}{n}\)
• \(\bigg(\frac{y}{x}\bigg)^2 \frac{m}{n}\)

4.

As shown in figure, a $70 kg$ garden roller is pushed with a force of $\vec{F}=200 N$ at an angle of $30^{\circ}$ with horizontal. The normal reaction on the roller is (Given $g=10 m s ^{-2}$ )

• $800 N$
• $600 N$
• $200 \sqrt{3} N$
• $800 \sqrt{2} N$

5.

A wire of length 'L' and radius 'r' is clamped rigidly at one end. When the other end of the wire is pulled by a force f, its length increases by 'l'. Another wire of same material of length '2L' and radius '2r' is pulled by a force '2f'. Then the increase in its length will be

• l
• 2l
• 4l
• \(\frac{l}{2}\)

6.

Potential energy is not defined for which of the following forces?

• Gravitational force
  
• Restoring force
  
• Friction
  
• Electrostatic force

7.

Force F depends on distance \(x\) and time \(t\) as \(F = ax^ 2 + bt\;\frac{1}{2}\) . Final dimension of \(\frac{b^2}{a}\) is

• \(M^{ - 1} L^2 T^{-3}\)
• \(M ^1 L^{ -3} T^3\)
• \(M^ 1 L^3 T^{-3}\)
• \(M ^2 L^ 2 T^1\)

8.

For the block shown, \(F_1\) is the minimum force required to move block upward and \(F_2\) is the minimum force required to prevent it from slipping find \(| F_1 - F_2|\)

• \(50 \sqrt{(3) N}\)
• \(5\sqrt{(3) N}\)
• \(25 \sqrt{(3) N}\)
• \(\bigg(5\sqrt{\frac{3}{2 N}\bigg)}\)

9.

A force of \(-P\hat k \) acts on the origin of the coordinate system. The torque about the point \((2, -3)\) is \(P(a\hat i+b\hat j)\), The ratio of \(\frac ab\) is \(\frac x2\). The value of x is -

10.

A heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle \(\theta\) with the horizontal. The weight experienced by the person is:

• \(\frac{W}{2}\)
• W
• \(W cos\theta\)
• \(W sin\theta\)

11.

A uniform wire has length L and radius r. It is acted on by a force F as shown. The elongation is l. If F and r are both halved, the new elongation will be :

• \(\frac{Δl}{2}\)
• \(Δl\)
• \(4Δl\)
• \(2Δl\)

12.

A balloon and its content having mass \( M \) is moving up with an acceleration \( a \). The mass that must be released from the content so that the balloon starts moving up with an acceleration \( 3a \) will be:

• \( \frac{2Ma}{3a + g} \)
  
• \( \frac{3Ma}{2a - g} \)
  
• \( \frac{3Ma}{2a + g} \)
  
• \( \frac{2Ma}{3a - g} \)
  

13.

Two forces \( \vec{F}_1 \) and \( \vec{F}_2 \) are acting on a body. One force has magnitude thrice that of the other force, and the resultant of the two forces is equal to the force of larger magnitude. The angle between \( \vec{F}_1 \) and \( \vec{F}_2 \) is \( \cos^{-1}\left(\frac{1}{n}\right) \). The value of \( |n| \) is _____.

14.

Force on a particle moving in a straight line is given by \( F = 6t^2\hat i - 3t\hat j\) and velocity is \(v = 3t^2\hat i + 6t\hat j\) . Find power at \(t = 2\).

• 216 W
• 108 W
• 0 W
• 54 W

15.

A body of mass of \(4\;kg\) experiences two forces \(\vec{F_1}=5\hat i+8\hat j+7\hat k \) and \(\vec{F_2}=3\hat i-4\hat j-3\hat k\) then acceleration acting on the body \(R\)