Question 1 A uniform ladder is put leaning against a rough vertical wall (coefficient of friction $0.5$), the bottom of the ladder being on a rough horizontal plane (coefficient of friction $0.4$). What is the least angle the ladder can make with the plane without slipping? Question 2 $ABCD$ is quadrilateral lamina in which $AB=3″$,... Read More

Question 1 $ABC$ is a triangle in which $BC=8″$, $\cos B = \frac{1}{2}$, $\cos C = \frac{11}{14}$. Forces of $3$, $12$, $7$ lb. wt. act along $BA$, $BC$, $CA$, respectively. How far from $B$ does the line of action of their resultant cut $BC$?. Find the magnitude of the resultant in lb. wt., correct to... Read More

Question 1 A mass of $21$ gm. is supported at $O$ by two light strings $OA$, $OB$ which are attached to fixed pegs at $A$, $B$, respectively, the straight line $AB$ being horizontal. If $AB=7$ ins., $AO=3$ ins., $BO=5$ ins., find the tensions in the strings. Question 2 Explain the terms “limiting friction”, “coefficient of... Read More

Question 1 A uniform rod $XY$, which weighs $12$ lbs., is supported by two strings $XZ$, $YZ$, attached to a fixed peg $Z$. If $XY=14″$, $XZ=9″$, $YZ=7″$, calculate the tensions in the strings. Question 2 $ABCD$ is a quadrilateral lamina. $AB=AD=12$ cm., $AC=15$ cm., $\angle BAC=30^\circ$ and $\angle ADC=90^\circ$. Find the perpendicular distance of the... Read More

Question 1 $ABC$ is a triangle in which $BC=5$ cm., $\angle BCA=30^\circ$, and $\cos ABC = \frac{3}{5}$. Forces of $10$, $8$, $6$ lb. wt. act along $BA$, $BC$, $CA$, respectively. If their resultant acts along the straight line $DE$, cutting $BC$ in $D$, calculate the length of $BD$ and the size of the angle $CDE$.... Read More

Question 1 If three co-planar non-parallel forces acting on a rigid body are in equilibrium, prove that their lines of action are concurrent and that the forces may be represented in magnitude and direction by the sides of a triangle taken in order. A uniform bar $AB$ which weighs $8$ lb. is supported by two... Read More

Question 1 A warship is travelling on a course $30^\circ$ East of North. To an observer on a liner travelling due East at $15$ knots the warship appears to be moving due North. Find the speed of the warship. In what direction should the warship travel at that speed so that it would appear to... Read More

Question 1 $A$ and $D$ are two fixed pegs in the same horizontal line. One end of a light string is attached to $A$ and the other end to $D$. The string carries a weight of $5$ lb. at $B$ and a weight of $X$ lb. at $C$. The angles $ABC$, $BCD$, $CDA$ are $135^\circ$,... Read More

Question 1 $A$ and $B$ are the ends of a uniform bar which is $8$ inches in length and which weighs $5$ lb. The bar is supported by two strings $AC$ and $BC$ attached to a fixed peg $C$. If $AC=5$ inches and $BC=4$ inches, find the tensions in the strings. What weight attached at... Read More