Two forces are such that the sum of their magnitudes is 18 N and their resultant is 12 N which is perpendicular to the smaller force. Then the magnitudes of the forces are (1) $12 \mathrm{~N} , 6 \mathrm{~N}$ (2) $13 \mathrm{~N} , 5 \mathrm{~N}$ (3) $10 \mathrm{~N} , 8 \mathrm{~N}$ (4) $16 \mathrm{~N} , 2 \mathrm{~N}$
If a body looses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest? (1) 1 cm (2) 2 cm (3) 3 cm (4) 4 cm
Speeds of two identical cars are $u$ and $4u$ at the specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is (1) $1 : 1$ (2) $1 : 4$ (3) $1 : 8$ (4) $1 : 16$
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
When forces $F_1, F_2, F_3$ are acting on a particle of mass $m$ such that $F_2$ and $F_3$ are mutually perpendicular, then the particle remains stationary. If the force $F_1$ is now removed then the acceleration of the particle is (1) $\mathrm{F}_1 / \mathrm{m}$ (2) $\mathrm{F}_2 \mathrm{~F}_3 / \mathrm{mF}_1$ (3) $\left(F_2 - F_3\right) / m$ (4) $\mathrm{F}_2 / \mathrm{m}$
A light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (vertically). If the acceleration of the system is $g/8$, then the ratio of the masses is (1) $8 : 1$ (2) $9 : 7$ (3) $4 : 3$ (4) $5 : 3$
Three identical blocks of masses $\mathrm{m} = 2 \mathrm{~kg}$ are drawn by a force $\mathrm{F} = 10.2 \mathrm{~N}$ with an acceleration of $0.6 \mathrm{~ms}^{-2}$ on a frictionless surface, then what is the tension (in N) in the string between the blocks $B$ and $C$? (1) 9.2 (2) 7.8 (3) 4 (4) 9.8
One end of a massless rope, which passes over a massless and frictionless pulley $P$ is tied to a hook $C$ while the other end is free. Maximum tension that the rope can bear is 360 N. With what value of maximum safe acceleration (in $\mathrm{ms}^{-2}$) can a man of 60 kg climb on the rope? (1) 16 (2) 6 (3) 4 (4) 8
A spring of force constant $800 \mathrm{~N/m}$ has an extension of 5 cm. The work done in extending it from 5 cm to 15 cm is (1) 16 J (2) 8 J (3) 32 J (4) 24 J
A ball whose kinetic energy is $E$, is projected at an angle of $45^\circ$ to the horizontal. The kinetic energy of the ball at the highest point of its flight will be (1) $E$ (2) $E / \sqrt{2}$ (3) $E / 2$ (4) zero
Two identical particles move towards each other with velocity $2v$ and $v$ respectively. The velocity of centre of mass is (1) $v$ (2) $v/3$ (3) $v/2$ (4) zero
Initial angular velocity of a circular disc of mass $M$ is $\omega_1$. Then two small spheres of mass $m$ are attached gently to diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc? (1) $\left( \frac{M+m}{M} \right) \omega_1$ (2) $\left( \frac{M+m}{m} \right) \omega_1$ (3) $\left( \frac{M}{M+4m} \right) \omega_1$ (4) $\left( \frac{M}{M+2m} \right) \omega_1$