164. According to the figure below, a body is at rest on a horizontal surface. A horizontal force $F = 40\,\text{N}$ is applied to the body. After $5$ seconds, the force $F$ decreases to $30\,\text{N}$. How does the body move after that? $$\left(g = 10\,\frac{\text{m}}{\text{s}^2}\right)$$
[Figure: A block of $2\,\text{kg}$ on a surface with $F = 40\,\text{N}$ applied horizontally; $\mu_s = 0.6$ and $\mu_k = 0.5$]

• [(1)] The body stops at that instant.
• [(2)] The body moves with acceleration $1\,\dfrac{\text{m}}{\text{s}^2}$.
• [(3)] The body moves with acceleration $2\,\dfrac{\text{m}}{\text{s}^2}$.
• [(4)] The body continues moving at constant speed.

The minimum velocity (in $\mathrm{ms}^{-1}$) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is
(1) 60
(2) 30
(3) 15
(4) 25

A smooth block is released at rest on a $45^\circ$ incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is
(1) $\mu_\mathrm{k} = 1 - \frac{1}{\mathrm{n}^2}$
(2) $\mu_\mathrm{k} = \sqrt{1 - \frac{1}{\mathrm{n}^2}}$
(3) $\mu_s = 1 - \frac{1}{n^2}$
(4) $\mu_s = \sqrt{1 - \frac{1}{n^2}}$

The upper half of an inclined plane with inclination $\phi$ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by
(1) $2\sin\phi$
(2) $2\cos\phi$
(3) $2\tan\phi$
(4) $\tan\phi$

A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force $\mathrm { F } = 20 \mathrm {~N}$, making an angle of $30 ^ { \circ }$ with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $\mu = 0.2$. The difference between the accelerations of the block, in case ( B ) and case ( A ) will be: ( $\mathrm { g } = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ )
(1) $3.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }$
(2) $0 \mathrm {~m} \mathrm {~s} ^ { - 2 }$
(3) $0.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }$
(4) $0.4 \mathrm {~m} \mathrm {~s} ^ { - 2 }$

Two blocks $A$ and $B$ of masses $m _ { A } = 1 \mathrm {~kg}$ and $m _ { B } = 3 \mathrm {~kg}$ are kept on the table as shown in figure. The coefficients of friction between $A$ and $B$ is 0.2 and between $B$ and the surface of the table is also 0.2 . The maximum force F that can be applied on B horizontally, so that the block A does not slide over the block B is : [Take $\mathrm { g } = 10 \mathrm {~m} / \mathrm { s } ^ { 2 }$ ]
(1) 16 N
(2) 12 N
(3) 40 N
(4) 8 N

Q3. A 2 kg brick begins to slide over a surface which is inclined at an angle of $45 ^ { \circ }$ with respect to horizontal axis. The co-efficient of static friction between their surfaces is:
(1) 1.7
(2) $\frac { 1 } { \sqrt { 3 } }$
(3) 0.5
(4) 1

Q4. A heavy box of mass 50 kg is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is :
(1) 1.47 N
(2) 147 N
(3) 14.7 N
(4) 1470 N